## 3 Data Description and Decomposition  
### Data Description  
The proposed scheme and the proposed model are validated on the monitoring wind speed data of two long-span cross-sea bridges. The investigated Bridge A is a cable-stayed bridge with a main span of 392 m, and the investigated Bridge B is a cable-stayed bridge with a main span of 428 m. Both the investigated Bridge A and Bridge B are in Zhejiang province, China, and the locations of these two bridges are shown in Figure 4. Wind speed data of both the investigated Bridge A and Bridge B are measured by three-dimensional ultrasonic anemometers, whose sample frequency are 10 Hz. Data of good integrity and quality are selected for model validation. Specifically, monitoring wind speed data from 1 January to 30 April 2018 are selected for the investigated Bridge A and are denoted as A2018, while monitoring wind speed data from 1 January to 30 April 2019 are selected for the investigated Bridge B and are denoted as B2019. The raw monitoring wind speed is transformed into the 10 min average wind speed data (original-resolution data) and the 1 min average wind speed data (high-resolution data) for both bridges. Time history plots of 10 min average wind speed data of A2018 and B2019 are shown in Figure 5, and corresponding descriptive statistics are summarized in Table 2.  
Figure 4: Locations of the investigated Bridge A and Bridge B: (**a**) Bridge A; (**b**) Bridge B. As shown in Figure 5, both A2018 and B2019 contain significant fluctuations. As shown in Table 2, A2018 and B2019 are of different characteristics. The maximum 10 min average wind speed of A2018 is 18.04 m/s and that of B2019 is 12.14 m/s, which are both above 10 m/s and can influence the serviceability of bridges. Both the maximum and mean wind speed of A2018 are larger than those of B2019. The standard deviation of A2018 is 3.21 m/s, which is also larger than that of B2019 and indicates fluctuations of A2018 are more significant. In addition, skewness and kurtosis of A2018 and B2019 indicate that distributions of 10 min average wind speed of A2018 and B2019 are deviated from Gaussian distribution. determined by comparing eigenvalue spectra, and the window length is determined by comparing results of denoising and influences of the end effect. The grouping parameter needs to be determined firstly for subsequent analysis, and eigenvalue spectra of different window lengths are shown in Figure 6. As shown in Figure 6, the first eigenvalue plays a dominant role in all the eigenvalue spectra, and the remaining eigenvalues are similarly small. This phenomenon indicates that the first eigen-triplet corresponds to the trend of the series and the remaining eigen-triplets correspond to noises for all the eigenvalue spectra, according to the assumption that the trend is the main component of the series, and the relative contribution to the series can be assessed by the relative value of the eigenvalue. As a consequence, the grouping parameter \(r\) is set to 1. The results of denoising of different window length are then compared, and the results are shown in Figure 7. As shown in Figure 7, SSA of different window lengths can denoise the raw series to varying degrees with the grouping parameter being 1, and the SSA of window lengths larger than 6 produces similar denoised trends. SSA of small window lengths, such as 2, tends to preserve more fluctuations, which can still contain unpredictable noise. Furthermore, SSA of large a window length, such as 8, tends to extract a smoother trend, which is easier to predict. The choice of window length also needs to take the end effect into consideration, and the end effects of different window length are shown in Figure 8. As shown in Figure 8, the influence range of the end effect increases with the increase in window length. To avoid the large computation caused by the introduction of long high-resolution series to compensate for the information loss, the influence range of the end effect should be kept at a small length.