Dynamic Prediction Model for Progressive Surface Subsidence Based on MMF Time Function

Abstract

It is imperative to timely and accurately predict the progressive surface subsidence caused by coal mining in the context of precision coal mining. However, the existing dynamic prediction methods that use time functions still have limitations, especially in the description of the moments of initiation and maximum subsidence velocity, which hinder their wide application. In this study, we proposed the MMF (Morgan–Mercer–Flodin) time function for predicting progressive surface subsidence based on the model assumptions and formula derivations. MMF time function can resolve the limitations in the description of the moments of initiation and maximum subsidence velocity perfectly. Afterward, we established the dynamic prediction model by combining the probability integral method with the MMF time function. Finally, using the measured subsidence data of working panel 22101 as an example, the accuracy and reliability of the dynamic prediction model was verified. The average RMSE and average relative RMSE (RRMSE) of prediction progressive subsidence using MMF time function are 46.65 mm and 4.63%, respectively. The accuracy is optimal compared with other time functions (for the average RMSE, Logistic time function is 80.57 mm, Gompertz time function is 79.77 mm, and Weibull time function is 90.61 mm; for the average RRMSE, Logistic time function is 7.66%, Gompertz time function is 7.73%, and Weibull time function is 8.62%). The results show that the method proposed in this paper can fully meet the requirements of practical engineering applications, achieve accurate dynamic prediction during the coal mining process, and provide good guidance for surface deformation and building protection.