PSI - Issue 64

F.-B. Cartiaux et al. / Procedia Structural Integrity 64 (2024) 285–292 Cartiaux / Structural Integrity Procedia 00 (2019) 000 – 000

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4.2.2. Cycle range counting Cycle range counting is released as a heat map as well, with the range of the cycles on the Y-axis and the color related to the number of cycles counted each week in each range category. The comparison of longitudinal strain cycle ranges for two similar locations on both decks is released in Fig. 6.

Fig. 6. Comparison of strain cycle ranges on the upper flange of the upstream and downstream decks.

The upstream deck, the oldest one, shows strain cycles with a range always above the one of the downstream deck, due to a different cross-section and to potential effects of its ageing on its bending rigidity. The exceptional convoy of April 20, 2023, on the upstream deck appears as an exception, but it is not the only one. At the opposite, the downstream deck shows no exceptional load and keeps a very constant distribution of the strain cycles. Horizontal patterns in the distribution of the strain cycles through time for both decks are an indicator for structural stability of their response to the traffic loads. Strain cycles with a range below 0.005 mm/m are not considered. 4.3. Wavelet analysis and data science methods applied to the events The strain and acceleration data have been made available for a team at Gustave Eiffel University to explore the possibilities of wavelet analysis and data science methods for the processing of synthetic health indices. The Continuous Wavelet Transform (CWT) is a time-frequency analysis tool that is very well suited for frequency and amplitude modulated signals. In the case of bridges under traffic, it allows for a precise analysis of their modal parameters over time, throughout the different parts of the signal. Moreover, it can be used to detect nonlinear behaviors. The CWT of a signal is computed from a convolution with a complex-valued function called the mother wavelet, that is shifted and dilated over time. It is particularly suitable for signals with modulated amplitude and frequency, which can be evaluated through the extraction of ridges , assuming the mother wavelet ψ has a null or sufficiently low Fourier transform in the negative frequencies domain. It can therefore be used for modal analysis of the free response of a system, including mode shapes for signals with multiple channels (Carpine et al., 2019). However, CWT analysis is a sensitive tool that needs fine adjustments to give precise modal results. In that respect, the main objective is to deduce from the CWT processing of measured accelerometric data, a “better” knowledge of the bridge mechanical behavior. Studying accelerometric data over almost 6 months show that indirect automatic processing data is insufficient without a complete model of the bridge including realistic characteristics of all existing components and ageing materials. It is then difficult to solve as we never have enough data from existing bridges to feed completely a representative numerical model. If the bridge seems undamaged (case of the 2 decks of the Jules Verne Bridge) without known referenced damage, the challenge is then to identify, from modal analysis, an evolution that could be representative of damage occurrence, without having a representative model of the bridge. What we try to obtain is a signature of the “normal” behavior of the existing bridge. In this study, we take information from all the raw data to find a global tendency of the whole data using data mining solutions. In the absence of a reference numerical solution on the structure, the classification method follows