PSI - Issue 62

Fabrizio Scozzese et al. / Procedia Structural Integrity 62 (2024) 911–915 Fabrizio Scozzese / Structural Integrity Procedia 00 (2019) 000 – 000

912

2

they appear quite vulnerable due to the level of degradation they are usually exposed to, in particular regarding the state of conservation of the precompression system (humidity into the protective sleeves, corroded tendons, etc.), whose degradation gradually increases in time (Podolny 1992, Wang 2023). The prestressing force and the cable path are usually designed to limit the structure cracking under service conditions and the system response is fundamentally linear, while deviations from the linear response arises only when the external loads attain high values close to the maxima considered in the design. Defects in the construction process or steel corrosion of the cables provide a reduction of the prestressing force and a rise of the nonlinearity of the response under travelling loads. Cracking usually close again once the load decreases and returns below a given threshold value. The system response can be classified as nonlinear elastic, and the transition between the initial stiffness and the reduced stiffness due to cracking is ruled by the intensity of the effective prestressing force. So the entire reliability of these systems is related to the cables healthy state, but the identification of the prestressing force and its monitoring over the time are not easy to be carried out. Indeed, lower input energy methods, e.g. operational modal analysis (Brincker and Ventura (2015)), are ineffective because the prestressing force does not affect the flexural stiffness in the linear response range, and a marginal influence can only be observed in more complex vibration modes (e.g. torsional modes), as widely demonstrated in theoretical and experimental studies (e.g., Dall'Asta and Leoni (1999), Saiidi et al. 1994, Dall'Asta (2000), Noble et al. 2016). Moreover, the healthy state of such components cannot be evaluated through visual inspection or conventional tests but special (expensive and complex) inspections are needed (e.g., DM 01/07/2022; CS 464 (2020); Federal Highway Administration-HRT-13-028 (2013)). In this paper, the abilities of the Hilbert-Huang Transform (HHT) (Huang 2014, Chen et al. 2014) are explored for the purposes of extracting the instantaneous property of vibration of the bridge and combine this information with a proper strain-energy measure (e.g., the displacement amplitudes) in order to characterize the nonlinear elastic response related to the prestressing force. A preliminary investigation on the capability of the method is performed analyzing the response of a simply supported beam with nonlinear elastic constitutive law subjected to travelling vehicles with different velocities and weights. A wider presentation of the method and results coming from an extensive parametric investigation can be found in the recent work of Scozzese & Dall’Asta (2024). 2. Method The idea presented in this study is that of exploiting HHT to evaluate the instantaneous frequencies of the system and to correlate them with a measure depending on the total strain energy (displacements are used in this work but other quantities, e.g., the curvature, could be used as well) in order to recover information on the current nonlinear elastic response. The proposed methodology requires the following three different tools to be performed: • Empirical Mode Decomposition EMD (Huang et al 1998), to extract the component of the motion carrying information on the system dynamic properties; • Hilbert Transform (HT) of the extracted dynamic component of the motion, required to enrich the signal with its imaginary part, permitting the extraction of the instantaneous properties of the motion; • Correlation between the instantaneous frequencies and the simultaneous response displacement amplitudes within a chart providing information on the system response nonlinearity. The combination of first and second tools, i.e., EMD and HT , is also known in the literature as the “Hilbert– Huang Transform” (HHT), and actually represents a signal processing technique developed by Norden and Huang (1998) for analyzing non-stationary and nonlinear signals. The information extracted through HT reveals fundamental to recovering the local information about the system response during the passage of a vehicle, indeed, the instantaneous angular velocity ( ) can be derived through differentiation of the phase angle. ( ) = ( ) (1)