Study on time series fitting curves for coal mining-induced surface subsidence

A fitting function suitable for surface subsidence time series curve is proposed based on the characteristics of the variable speed of the surface subsidence after coal seam mining. The influence of fitting parameters b and c on curve shape, subsidence velocity and acceleration are analyzed. The calculation program was compiled with 1stOpt 1.5 Software, and a time series curve of surface subsidence caused by coal seam mining was measured and compared with other three types of fitting functions. The research results show that the proposed mathematical formula of the fitting function is simple and the number of parameters is moderate. From the aspects of sinking curve shape, sinking speed and sinking acceleration, it is consistent with the dynamic process of surface subsidence in coal seam mining. The fitting function has high fitting precision to the measured curves, and the correlation coefficient of the fitting is 0.9968. The maximum sinking amount predicted by the fitting function is 468.7 mm, and the calculated maximum sinking speed is 0.325 mm/d, and the corresponding time is 594.3 d, which are all close to the measured value.