Vehicle’s wheels were mostly modeled as a point, which can touch the valleys of pavement roughness, creating unrealistic high-frequency oscillation. This can be avoided by using the disk model for the wheels, which however adds significant complexity to the vehicle–bridge interaction (VBI) analysis. In this paper, a refined roughness formula is generated to account for the wheel size effect such that it can be used by point model. Still, the low-frequency part of the roughness presents some masking effect on the bridge scanning by the test vehicle. To this end, two countermeasures are suggested, i.e. residual response and traffic flows. This study has demonstrated that: (1) the roughness generated by the refined formula can reflect the trace of the disk model; (2) the refined formula facilitates the VBI analysis by using the point model; and (3) the two countermeasures for roughness are effective for improving the scanning of bridge frequencies.
Studying frequency domain representation for the coherence between two signals is an important basic theoretical problem in the fundamental theories of signal processing. However, magnitude-squared coherence function (MSCFs) could lose some phase information. Based on the core theorem in the frequency domain coherence theories, called as double spectral theorem (DST), we presented the two types of new magnitude coherence functions (MCFs), called as the same type magnitude coherence function (SMCF) and the difference magnitude coherence function (DMCF) respectively, which had been mathematically derived from DST and the conditions that they are equal to 1 or -1 or 0 were theoretically derived from DST. Here, we further demonstrated that SMCF and DMCF could be used to exactly extract the coherence between two signals by each component.
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