DUN Z L，DU H G，ZOU Y F，et al. Application of Tanh time function in prediction of surface subsidence in goaf  [J]. Journal of Henan Polytechnic University(Natural Science), doi: 10.16186/j.cnki.1673-9787.2024030077.

Received：2024-03-18

Revised：2024-10-11

Online：2025-01-19

Application of Tanh time function in prediction of surface subsidence in goaf (Online)

DUN Zhilin^1，2，DU Haiguang^1，3，ZOU Youfeng⁴，DUN Zhiyuan⁵，REN Lianwei^1，2，

WANG Wenchang⁶，CHEN Shaojie⁷

(1. School of Civil Engineering, Henan Polytechnic University, Jiaozuo 454000, Henan，China; 2. Henan Engineering Research Center for Ecological Restoration and Construction Technology of Goaf Sites, Jiaozuo 454000, Henan ，China;3. School of Traffic Engineering, Huanghe Jiaotong University,Jiaozuo 454950, Henan ，China; 4. School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, Henan ， China; 5. School of Civil and Architecture Engineering, Jiaozuo University, Jiaozuo 454000, Henan ， China;6. College of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, Henan, China; 7. College of Energy and Mining Engineering, Shandong University of Science and Technology, Qingdao 266590 , Shandong，China)

Abstract: Objectives In response to the individual time function model with unsatisfactory prediction effect and insufficient reliability as well as the difficulty of calculating weights in the variable weight combination model in the existing methods for dynamic prediction of surface subsidence in the goaf site. Methods Firstly, the hyperbolic tangent function (Tanh) is introduced and optimized to derive a two-parameter Tanh time function applied to surface subsidence prediction, the parameter influence on the surface subsidence, subsidence velocity and subsidence acceleration curve morphology of Tanh time function is analyzed, and the method of identifying function parameters is given. Secondly, the variance reciprocal method equal-weight combination model and the error square sum reciprocal method variable-weight combination model are established for surface subsidence prediction analysis. Finally, the combination models are combined for prediction and used in the goaf surface example of Qianjiaying Coal Mine 1176 east working face. Results The results show that for point 23, the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) of the Tanh time function model are 35.03, 28.192, and 0.102, respectively, which are smaller than the corresponding indexes of the commonly used MMF time function model. In addition, the root mean square error (RMSE) and mean absolute error (MAE) of the 2 combination models are smaller than those of the single time function models in their combinations, in which the RMSE, MAE, and MAPE of the variable weight combination model of the squared sum of errors and the inverse method are the smallest among the 4 models. Conclusions The Tanh time function model proposed in this paper is capable of realizing effective dynamic prediction of goaf surface subsidence. The calculation of variable weights in the error square sum reciprocal method variable-weight combination model is simple and efficient, and shows better prediction accuracy and stability compared to the variance reciprocal method equal-weight combination model. The predicted values of subsidence in the complex change interval of the goaf surface are remained approximately the same as the measured values. It is indicated that the application of the combined model is more superior in the dynamic prediction of goaf surface subsidence.

Key words：goaf site; surface subsidence; hyperbolic tangent time function; the error square sum reciprocal method variable-weight combination model

CLC: TD325.2