当采空区场地进行高速铁路修建时，地表沉降动态精准预测和剩余变形计算对高速铁路的 工程建设及安全运行尤为重要。 针对单项时间函数在复杂采空区地表沉降动态预测中存在着适用 范围有限、预测准确性和稳定性不高的问题，对 Knothe、Weibull、Logistic 与 MMF 时间函数的曲线形 态及参数物理意义进行了分析;为获取时间函数参数的全局最优解，建立了基于果蝇优化算 法(Fruit Fly Optimization Algorithm，FOA)和模拟退火算法(Simulated Annealing Algorithm，SAA)的 混合算法;引入以最小误差平方和为准则的最优非负变权组合模型，并构建了 Knothe-Weibull、 Knothe-Logistic 与 Knothe-MMF 等 6 种不同的双项时间函数组合模型。 并在地表沉降预测的基础 上，给出了采空区场地剩余变形的计算方法。 结果表明:所提出的混合算法具有收敛状态稳定、求 解精度高的优点，适用于时间函数参数的求解问题。 组合模型在预测准确性和稳定性上均优于组 合中的单项时间函数，能够突破单项时间函数在复杂地质采矿条件预测效果不佳的局限性，较好地 提升时间函数在预测中的精准度和适用度。 此外，组合模型在已临近实测沉降值的情况下扩展了 预测曲线的有效区间，并借助变权系数将单项时间函数在有效区间的信息进行筛选并重组，得到全 程吻合实测沉降值的最优沉降预测曲线。 其中，Knothe-Logistic 函数模型的均方根误差(RMSE)、 平均绝对误差(MAE)、平均绝对百分比误差(MAPE)在 3 次预测中均最低，有效地解决厚松散层、 薄基岩、浅埋煤层条件下采空区地表沉降动态精准预测问题。 组合模型可为实现采空区场地高速 铁路建设前地表沉降的稳定、高精度动态预测提供参考。 通过基于 Knothe-Logistic 函数计算不同 时刻地表点剩余变形得到的变化规律与实际开采过程相符合，剩余变形作为采空区场地地基变形 的重要组成部分，可为采空区场地高速铁路建设的可行性评价提供一种依据。

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.