Dynamic prediction of goaf surface subsidence and calculation of residual deformation based on time function combination model

When the construction of high⁃speed railway is carried out in goaf site，the dynamic and accurate prediction of surface subsidence and residual deformation calculation are especially significant for the engineering construction and safe operation of high⁃speed railway.Aiming at the problems of limited applicability，low prediction accuracy and stability of the individual time functions in dynamic prediction of surface subsidence in complicated goaf，the curve forms and the parameters physical significance of Knothe，Weibull，Logistic and MMF time function are analyzed.A hy⁃ brid algorithm based on fruit fly optimization algorithm (FOA) and simulated annealing algorithm (SAA) is estab⁃ lished to acquire the global optimum of the time function parameters.The optimal non⁃negative variable weight combi⁃ nation models with the minimum error sum of squares as the criterion is introduced，and six different two⁃term time function combination models，such as Knothe⁃Weibull，Knothe⁃Logistic and Knothe⁃MMF，are constructed.Based on the prediction of surface subsidence，the calculation method of the residual deformation in goaf site is provided.The results show that the proposed hybrid algorithm has the advantages of stable convergence state and high solution accuracy，and is appropriate for the solution of the time function parameters.The combination models outperform the individual time functions in the combination in terms of prediction accuracy and stability，can break through the limitation of the inferi⁃ or prediction of the individual time functions in complex geological and mining conditions，and better upgrading the ac⁃ curacy and applicability of the time function in prediction.In addition，the combination models extend the valid interval of the prediction curve in the case that the measured subsidence value has been approached，and the information of the individual time functions in the valid interval is filtered and reorganized with the assistance of variable weight coeffi⁃ cient to obtain the optimal subsidence prediction curve that matches the measured subsidence value throughout. In which，the root mean square error (RMSE)，mean absolute error (MAE)，and mean absolute percentage error (MAPE) of Knothe⁃Logistic function model are the lowest among the three times prediction，which can effectively solve the problem of accurate dynamic prediction of surface subsidence in goaf under the conditions of thick loose layer，thin bedrock，and shallow coal seam.The combination models can provide a reference for realizing stable and high precision dynamic prediction of surface subsidence before the construction of high⁃speed railway in goaf site. The change law obtained by calculating residual deformation of surface points at different moments based on Knothe⁃Logistic function is consistent with the actual mining process，and residual deformation，as an important part of the foundation deformation in goaf site，can provide a basis for the feasibility evaluation of high⁃speed railway con⁃ struction in goaf site.