老采空区残余沉降的离散灰色预测模型

针对老采空区残余沉降序列波动性较大、传统灰色模型预测效果差的不足,建立了残余沉降的多变量离散灰色预测模型(DGM(2,2)),取阶次为2以适应残余沉降的波动变化,选择残余沉降值作为沉陷系统的主行为因子,而将空气、地下水等外界渐变因素对沉陷系统的综合影响作为相关因子,并按等时间影响原则进行量化。通过实例将DGM(2,2)模型的预测结果与6种传统灰色预测模型作对比分析。结果表明:DGM(2,2)预测模型在拟合优度、预测精度和稳定性等方面明显优于传统灰色预测模型,且建模过程避免了微分方程的解算,降低了计算复杂度。

Discrete grey prediction model of old goaf residual subsidence

Based on analyzing the effect factors of residual subsidence of old goaf, a new prediction model named discrete grey model of 2 order 2 variables (DGM(2,2)) is set up. In this model, the order of 2 provides a better simulation for the fluctuating residual subsidence series, the 2 variables express the principal factor and the associated factor of the subsidence system, the first is the series of residual subsidence which is the principal factor, the other is the combined effect of external conditions, such as air, groundwater, which quantified according to the equal time-effect principle. The modeling process is discussed in detail, and an example is given to compare the new model with six traditional grey models. The results show that: the goodness of fit, prediction accuracy and stability of DGM(2,2) are obviously superior to the six grey models; the modeling process is simple, and its prediction results are accurate and reliable. Thus, DGM(2,2) can be applied in residual subsidence prediction of old goaf.