# The Fractal Characteristics of Ground Subsidence Caused by Subway Excavation
## 6 Conclusions  
This paper presented a denoising model for reducing the noise of monitoring data based on wavelet transform theory. The fractal characteristics of the surface settlement caused by subway excavation were analyzed by applying fractal theory. The noise reduction effect of the model was evaluated by comparing it under different wavelet functions, decomposition levels, threshold functions, and threshold rules. The optimal noise reduction model for surface settlement data was identified. In the fractal interpolation phase, the original monitoring curves were divided into two stages (i.e., the period of significant deformation and the period of insignificant deformation), and nine interpolation points were selected in each stage (i.e., 18 interpolation points were selected from the 99 in the original monitoring data). The effects of missing data and outliers were overcome by using the fractal interpolation method. The fractal dimension of the monitoring curves under different monitoring frequencies was calculated in the fractal characteristics section using the box-counting method. This was followed by an analysis of the relationship between the fractal dimension and surface settlement. The conclusions were as follows:  
Figure 14: The deformation varies with monitoring frequency.  
Figure 15: The fractal dimension varies with monitoring frequency.  
When utilizing the dbN wavelet function, a decomposition level of 1, the hard threshold method, and the rigrsure threshold rule, the noise reduction model exhibited a high SNR and a low RMSE and exhibited the most effective noise reduction in this instance.
2. The daily surface deformation data were derived by fractal interpolation, and 291 data points were successfully extracted from 18 interpolated points, which compensated for the effects of missing data and outliers, to a certain extent. This method effectively captured the actual deformation information with an average relative error of only 13%.
3. The fractal dimension of the monitoring curves was consistently greater than 1, indicating that the surface deformation caused by the construction of the Urumqi subway was self-similar. Additionally, as the monitoring frequency decreased, the fractal dimension exhibited a declining trend, and the surface settlement and deformation curves tended to smooth, accompanied by a concurrent decrease in the actual information that could be captured.  
It is important to note that, while the research method employed in this paper is effective in the case of the Urumqi Railway Transit Line 1, further studies are necessary to assess its efficacy in other projects. Additionally, this paper only examines the fractal characteristics of surface settlement under varying monitoring frequencies. However, surface settlement is a complex process, and future research will consider a wider range of factors for improvement.  
Conceptualization, P.H. and Y.Q.; methodology, P.H.; software, P.H. and L.X.; validation, P.H. and J.Z.; formal analysis, P.H. and J.Z.; investigation, P.H. and L.X.; resources, Y.Q.; data curation, P.H. and J.Z.; writing--original draft preparation, P.H.; writing--review and editing, P.H. and J.Z.; visualization, Y.Q. and L.X.; supervision, Y.Q.; project administration, Y.Q.; funding acquisition, Y.Q. All authors have read and agreed to the published version of the manuscript.  
This study has been funded by the Natural Science Foundation of Xinjiang Uygur Autonomous Region, Research on data mining and surface subsidence prediction of subway construction deformation monitoring based on big data (Project Number 2021D01C073).  
Not applicable.  
All data generated and analyzed during this study are included in this article.  
Author [PERSON] is employed by Xinjiang Transportation Investment (Group) Co. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.