*5.1. Power Spectral Density*

Power Spectral Densities (PSDs) refer to the spectral energy distribution per unit of time. PSDs focus on various features of the signal in the frequency domain, intending to extract useful signals in frequency domains that are drowned in noise. Based on Fourier transform, the PSDs of the annual temperatures of the girder surface temperature could be

calculated. Taking a typical section S6 for an example, the results of the top and bottom plates are shown in Figure 13.

**Figure 13.** The PSD of the measured annual temperature. (**a**) Top plate measurement points; (**b**) Bottom plate measurement points.

There are two prominent peaks that can be observed in the PSD of Figure 13. The period of the first peak was 24 h, which was identical to the daily period. The period of the second peak was 12 h, which was induced by the transmission from day to night. The results of PSD analysis show that the daily temperature could be considered a representative sample of the annual temperature. Moreover, the daily temperature could provide a more detailed view of the temperature change process compared to the annual temperature. Therefore, the temperature in one day can be selected to investigate the mechanisms and processes of longitudinal temperature gradients.

In addition, the PSD generally decreased with the increase in frequency and tended to become a horizontal line in the high-frequency region. The general decreasing trend resulted from a reduction in the high-frequency components of temperature. When this frequency was high enough, the temperature did not change in the corresponding short period. Thus, the PSD was almost horizontal in the high-frequency region. These results indicate that the surface temperature of the steel box girder was mainly controlled by low-frequency components, and the high-frequency effect was less affected.
