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基于SSA-多元时序融合的矿井涌水量预测模型

刘杰1,2, 杨晓1, 高红星2, 马明2, 和志永3, 任岩4

1.山东科技大学 地球科学与工程学院，山东 青岛  266590；2.滕州郭庄矿业有限责任公司，山东 滕州  277519；3.山东能源集团 西北矿业有限公司，陕西 西安 710026；4.中铁二十五局集团 第三工程有限公司，湖南 长沙  410001

摘要: 目的为解决复杂条件下矿井涌水量预测确定性分析方法获取水文地质参数困难，不确定性分析方法需进一步刻画涌水量变化特征等问题，开展基于SSA-多元时序融合的矿井涌水量预测模型研究。  方法依据研究区20 a涌水量数据绘制图表并分析涌水量序列的集中趋势、离散程度和分布情况，采用奇异谱分析（singular spectrum analysis，SSA）提取其趋势、波动、噪声成分，并针对不同信息成分采用不同模型拟合预测。首先，基于奇异谱迭代插补思想，借助MATLAB软件编写内外循环代码，通过设置相邻序列的残差、相关系数阈值确定循环次数，建立趋势序列预测模型；其次，依据波动、噪声序列等变化特点，采用基于贝叶斯信息准则确定的ARIMA和SARIMA时间序列模型预测，并通过白噪声检验评价其拟合效果；最终通过线性融合3种模型的预测结果即可获得所需预测值。  结果 计算多手段融合预测模型和单一模型分别与原始序列的决定系数（R²）以及平均误差百分数（MAPE）发现，多手段融合预测模型的R²及 MAPE分别为94%，2.34%，均优于单一模型的74%，6.8%。  结论与单一模型（R²=74%， MAPE=6.8%）相比，多手段融合预测模型的R²达94%， MAPE降至2.34%，拟合精度显著提升，能更准确地刻画研究区矿井涌水量的时序变化特征。

关键词:矿井水;矿井涌水量预测;数据分析;奇异谱分析;时间序列分析

doi:10.16186/j.cnki.1673-9787.2024100020

基金项目:国家自然科学基金资助项目（41572244）

收稿日期:2024/10/14

修回日期:2025/06/10

出版日期:2026-07-24

A mine water inflow prediction model based on SSA and multivariate time-series fusion

Liu Jie1,2, Yang Xiao1, Gao Hongxing2, Ma Ming2, He Zhiyong3, Ren Yan4

1.College of Earth Science and Engineering， Shandong University of Science and Technology， Qingdao  266590，  Shandong， China；2.Tengzhou Guozhuang Mining Co.， Ltd.， Tengzhou  277519， Shandong，  China；3.Shandong Energy Group Xibei Mining Co.， Ltd.， Xi'an  710026， Shaanxi， China；4.China Railway 25th Bureau Group Third Engineering Co.， Ltd.， Changsha  410001， Hunan， China

Abstract: Objectives To address the difficulty in obtaining hydrogeological parameters in deterministic prediction methods under complex conditions， and the limitations of uncertainty-based approaches in characterizing variations in mine water inflow， a prediction model based on SSA and multivariate time series fusion was developed.  Methods Based on 20 years of mine water inflow data from the study area， descriptive statistical analyses were performed to examine the central tendency， dispersion， and distribution features of the inflow series. Singular spectrum analysis （SSA） was applied to decompose the series into trend， fluctuation， and noise components， and different models were adopted to forecast each component. First， based on the iterative imputation concept of SSA， inner and outer loop algorithms were implemented in MATLAB. The number of iterations was determined using residuals and correlation coefficients between adjacent reconstructed sequences， thereby establishing the trend forecasting model. Second，  according to the characteristics of fluctuation and noise components， ARIMA and SARIMA models selected based on the Bayesian information criterion （BIC） were employed for prediction， and model performance was evaluated using white-noise tests. Finally， the final prediction results were obtained by linearly combining the outputs of the three models.  Results The coefficient of determination （R²） and mean absolute percentage error （MAPE） indicate that the proposed fusion model achieved an R² of 0.94 and a MAPE of 2.34%， outperforming the single-model approach （R²=0.74， MAPE =6.8%）. Conclusions Compared with the single model （R²=74%， MAPE =6.8%）， the multi-method fusion prediction model achieves an R² of 94% and a reduced MAPE of 2.34%. The fitting accuracy is significantly improved， enabling a more accurate characterization of the temporal variation characteristics of mine water inflow in the study area.

Key words:mine water;mine water inflow prediction;data analysis;singular spectrum analysis;time-series analysis