PSI - Issue 64

Kun Feng et al. / Procedia Structural Integrity 64 (2024) 596–603

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Kun Feng et al. / Structural Integrity Procedia 00 (2019) 000 – 000

In the analysis of the bus vehicle fleet, a Monte Carlo Simulation was employed to stochastically determine the weight of the bus or the number of seated passengers. A loading scenario where 50% of the seating capacity is utilized, equating to 37 passengers at 68 kg each, sets the mean bus vehicle weight at 16900 kg. A standard deviation of 800 kg was assumed for this weight distribution. Fig. 2 illustrates the normal distribution curve of the bus vehicle weights and highlights the corresponding frequencies of buses within a fleet of 100000 units, as determined through eigenvalue analysis in MATLAB (González, Feng et al. 2022).

Fig. 2. Histogram plot of a vehicle fleet with 100000 bus vehicles, (a) bus vehicle weight, (b) 1 st vehicle frequency, (c) 2 nd vehicle frequency.

3. Research Methodology Operating Deflection Shape (ODS) analysis, or operational deflection shape analysis, is pivotal in structural vibration analysis, delineating how a structure deflects at a specific frequency to a particular point. This paper leverages differences in ODS patterns between healthy and damaged bridge structures to identify and localize damage, specifically cracks (Sinha, Friswell et al. 2002). The proposed research methodology unfolds in three steps: (1). To obtain the accelerations of the contact point response: an efficient approach has been developed in our previous research (Feng, Casero et al. 2023), where the contact point accelerations can be easily obtained from measured vehicle accelerations through using transfer function algorithms. Alternative approaches to extract contact point responses can be referred to (Erduran and Gonen 2024). Therefore, in this paper, the contact point accelerations due to vehicle crossing are assumed to be known. (2). To decompose the obtained contact point accelerations into several Intrinsic Mode Functions (IMFs): in this paper, variational mode decomposition is selected for mode decomposition due to its excellent noise resistance and better decomposing performance. Detailed algorithms about the variational mode decomposition applied in bridge structures can be referred to (Li, Guo et al. 2022), (Abuodeh and Redmond 2023). (3). To calculate the analytic signal for the selected IMF: the Hilbert transform is used in this paper for computing the analytic signal, and its absolute value is adopted as the final ODS curve. Details of applying the Hilbert transform for computing the analytic signal can be found in reference (Quqa, Giordano et al. 2022). As described in Step 2, Fig. 3 illustrates the results of applying variational mode decomposition, utilizing the ' ' function within MATLAB for the analysis of a 3-second contact point acceleration. In this study, the decomposition was configured to yield 10 Intrinsic Mode Functions (IMFs). Notably, the 10 th IMF reveals crucial insights related to the first mode, encapsulating bridge-related information. This information is characterized by an estimated frequency of 5.68 Hz, accompanied by a minimal relative error of 0.35%, compared to the 1 st bridge frequency listed in Table 1.