30 L. Sibille et al. component is the one mostly due to noise. The results obtained by applying PCA to the first natural frequency and tidal levels are shown in Fig. 7c. It is observed that the largest variability represented by the the first principal component (blue dots and line in Fig 7c), is primarily due to the tidal fluctuations. The Pearson correlation coefficient between the tidal level and the first principal component is -0.98, confirming the very high inverse correlation between the two. Finally, Fig 7d presents a comparison between the first identified natural frequency (blue dots and line) and the adjusted natural frequency (red dots and line) after removing the first principal component. From the plot, it is evident that the first identified natural frequency fluctuates between approximately 2.3 Hz and 2.6 Hz. After the adjustment, the natural frequency stabilizes, fluctuating in a narrower range around 2.45 Hz, which is close to the natural frequency of the FEM model. The reduction in fluctuation indicates that the tidal effects have been largely removed, and the adjusted natural frequency is now predominantly influenced by other operational and environmental variabilities, such as temperature, wind, and wave height. It is worth clarifying that this analysis is based on the assumptions that: the different sensors used are affected by the same noise; the signal can be decomposed as a combination of linear independent set of principal components; the first one is mainly due to the tidal effect. Conclusions This paper presents the SHM system implemented at the Magerholm ferry quay, developed as part of a collaboration between Møre og Romsdal County and NTNU. The SHM system comprises 22 accelerometers, 2 GPS antennas, and 1 thermometer, all connected through wires to two logger units and a router for data transmission. An AOMA algorithm was used to identify the daily variation of the modal parameters of the linkspan over a six-month period. The environmental effects on the first natural frequency of the linkspan were investigated, with a particular focus on tidal levels. The analysis revealed a significant inverse linear relationship between tidal levels and the first natural frequency, with a Pearson correlation coefficient of -0.83. Least Squares Regression was applied to quantify this relationship. Additionally, PCA was applied to the first natural frequency and tidal levels, showing that the first principal component is mainly caused by the tidal levels. After removing the first principal component, the resulting adjusted natural frequency displays fluctuations. These fluctuations are likely caused by changes in stiffness due to varying boundary conditions, specifically related to the hydraulic lifting towers and conical fenders, which change their mechanical properties based on the inclination of the linkspan. Additionally, other environmental and operational factors may also contribute. Even though the AOMA might have resulted in inaccurate estimates of the modal properties, as the assumption of uncorrelated white noise excitation across the structure was violated by tidal levels and operational loads during the linkspan’s adjustment phase, this is a preliminary study aimed at exploring the influence of tidal levels on the structure. Further analysis should focus on applying SI techniques capable of handling non-white noise assumptions to improve the accuracy of modal parameter identification under these complex environmental and operational conditions. This preliminary analysis lays the groundwork for the application of more advanced techniques, such as the Hybrid Operational Modal Analysis [16] and Multivariate Nonlinear or Metric Learning approaches [17], to a broader dataset that includes additional environmental variabilities such as temperature, wind, and waves. These advanced techniques can help further filter out the environmental effects, improving the accuracy of the modal parameter identification and enhance structural analysis including FEM Updating, SI, and Damage Detection. Acknowledgments The study was conducted with support from the Research Council of Norway through the Norwegian Regional Research fund in Møre og Romsdal county (SHMBru project 331578 and SARTORIUS project 353029). The authors gratefully acknowledge the Møre og Romsdal fylke for financing the research and for helping during the planning and execution of instrumentation and measurements. References 1. Siedziako, B., Fenerci, A., and Nord, T.S. “Experimental vibration analysis on the rykkjem ferry dock during ferry berthing”. In Society for Experimental Mechanics Annual Conference and Exposition, pages 103–111. Springer (2023). 2. Siedziako, B., Nord, T., and Fenerci, A. “Finite element model updating of a ferry dock bridge”. Journal of Physics: Conference Series, 2647:182001 (2024). 3. Sibille, L., Nord, T.S., Siedziako, B., and Fenerci, A. “Impact force identification on a ferry dock bridge”. Journal of Physics: Conference Series, 2647(18):182012 (2024). 4. Vegvesen, S. “Brutus - management system for bridges, ferry quays and other load-bearing structures in norway” (2023). 5. Olivieri, C., Fortunato, A., and DeJong, M. “A new membrane equilibrium solution for masonry railway bridges: the case study of marsh lane bridge”. International Journal of Masonry Research and Innovation, 6(4):446–471 (2021).
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