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Accuracy of instantaneous frequencies predicted by the Hilbert-Huang transform for a bridge subjected to a moving vehicle
Published in Hiroshi Yokota, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Life-Cycle Sustainability and Innovations, 2021
M. Casero, A. González, E. Covián
When using field measurements, the mass and stiffness matrixes will not be available, and it becomes necessary to employ a signal processing tool in the time-frequency domain that will characterize the time-varying frequencies of the system. Some of the most popular signal processing tools are the Short-time Fourier Transform (STFT), Continuous Wavelet Transform (CWT) and Hilbert-Huang Transform (HHT). The STFT is an extension of the FFT that uses a moving window to obtain instantaneous frequencies and to achieve a time-frequency domain representation. However, the selection of the window size may be challenging, since it leads to a trade-off between the time and frequency resolutions (Amezquita-Sánchez & Adeli 2016). The CWT is widely used due to its versatility and computational efficiency. Cantero & Obrien (2013) test several mother wavelets for the CWT on the simulated response of a beam traversed by a sprung mass, to investigate the variation of the 1st natural frequency with the position of the vehicle. Their results indicate that the maximum variation of the frequency happens when the vehicle is located at midspan, which is the point of maximal modal amplitude for the 1st mode. They also find that the magnitude of the frequency variation is linked to the mass and frequency ratios between the sprung mass and the beam. Higher mass ratios and frequency ratios closer to one lead to more significant frequency variations. Lab experiments (Cantero et al. 2019) and field tests (Cantero et al. 2017) provide further experimental evidence on the variation of the forced frequency.
Variations in local, transported, and exposure risks of PM2.5 pollution: Insights from long-term monitoring data in mega coastal city
Published in Human and Ecological Risk Assessment: An International Journal, 2022
Pavanaditya Badida, Jayapriya Jayaprakash
Concentration weighted trajectory (CWT) is used for weighing trajectories with associated concentrations (Hsu et al. 2003; Squizzato and Masiol 2015). CWT accounts for the residence time of trajectories. Every gridded cell is assigned a weighted-concentration that is obtained by averaging the concentrations that have associated trajectories crossing the grid cell. CWT effectively highlights the relative significance of potential sources contributing to pollution at the receptor sites. CWT is represented by Eq. (2). where is the concentration weighted trajectory, is the concentration associated with trajectory end-points in the i, jth cell, and is the residence time of the trajectory endpoints in the i, jth cell.