PSI - Issue 62

Valentina Giglioni et al. / Procedia Structural Integrity 62 (2024) 887–894 Giglioni et al. / Structural Integrity Procedia 00 (2019) 000–000 3 probability distribution ( ) , = { } = 1 indicating a finite sample set from . For a fixed domain, a related task = { , ( ∙ )} can be identified with a label space and a predictive function ( ∙ ) . Given these premises, DA is the process to improve the target predictive function ( ∙ ) in t using the knowledge previously extracted from the source domain , assuming = and = . In this particular application (see Fig. 1), the source domain coincides with a certain span of the bridge, for which both healthy and damage features are labelled, while the target domain is associated to a different span, whose damage information may not be available. Therefore, the idea is to acquire data from a monitored bridge, extract damage sensitive features (e.g., natural frequencies) and build a shared feature space via DA to find a mapping in data distribution. By employing the transformed features, any ML algorithm can be trained using labels describing damage on one span (e.g., span X) to identify the same damage occurring in a second span (e.g., span Y). 889

Fig. 1. General flowchart of the methodology

The adopted DA strategy, involving a two-step alignment has been already introduced in Giglioni et al. (2023). Normal Condition Alignment (NCA), presented in Poole et al. (2023), is firstly employed to statistically align healthy data of source and target domains, in terms of means and standard deviations. The Joint Domain Adaptation (JDA) technique, developed in the context of kernel-based DA methods, is afterwards used to refine and facilitate the transfer by learning a non-linear transform from the feature space to a Reproducing Kernel Hilbert Space (RHKS) that minimises the distance between the joint distributions. The process ends with the generation of latent features, that extract and enclose the main information of the investigated datasets. Extensive details on such DA techniques are provided in references (Gardner et al. (2021), Poole et al. (2023)). 3. Description of the experimental model bridge The mock-up bridge, illustrated in Fig. 2, was built inside the structural dynamics Laboratory for Verification and Validation (LVV) of the University of Sheffield. The model lies on a 3 m x 2 m shake table, utilised to reproduce random input vibrations in a frequency range between 5 and 110 Hz. The main deck has a global length of 2990 mm, a thickness of 2 mm and a width of 270 mm. Four continuous aluminium “I” beams are bonded to the deck, while piers are constructed from aluminium Bosch-Rexroth sections and clamped via two steel plates, that are connected with Belleville washers to allow variable connection stiffness between the ground and the pier (Fig. 2c). Regarding the deck/pier joints, flanged deep-groove ball bearings are clamped to the “I”-beam section, preventing lateral displacements and allowing any movement (and thus any pier spacing required by the user) along the axial length of the bridge deck. To allow thermal expansion and motion from any induced vibration, the longitudinal movement is locked on just one of the end supports, while the intermediate supports and un-fixed end are free to roll axially. As indicated in Fig. 1, some additional masses are homogeneously distributed along the deck. Note that the monitoring system globally includes (i) twenty-two accelerometers (measuring responses in the vertical direction), twenty of which are located on the deck, i.e., A1-A20, while two additional sensors, i.e., A21-A22, in one pier (Fig. 2b an 2d), and (ii) a thermocouple to provide the updated values of temperature during the experimental tests. Specifically, the environmental chamber is set to reproduce a wide range of temperatures, from -15°C to +30°C. Each test consists in collecting consecutive ∼ 20 seconds-long repeats with a sampling frequency of 256 Hz. Table 1 summarises the geometry of different bridge configurations, generated by changing the position of the piers in the longitudinal direction and slightly varying the surface layer on the deck. In this paper, the attention is focussed