不同时间序列模型在岩溶山区矿井涌水量预测中的应用

邹银先; 褚学伟; 段先前; 刘埔; 王中美; 王益伟

doi:10.11932/karst2023y031

不同时间序列模型在岩溶山区矿井涌水量预测中的应用

doi: 10.11932/karst2023y031

1.
贵州省地质环境监测院, 贵州贵阳 550081
2.
贵州大学资源与环境工程学院, 贵州贵阳 550025

基金项目: 贵州省科技支撑计划（黔科合支撑[2017]2858）；贵大人基合字（2019）36号

详细信息

作者简介:
邹银先（1985－），男，高级工程师，主要从事水文地质、环境地质研究工作。E-mail：812526840@qq.com

通讯作者:
褚学伟（1979－），男，博士，讲师，主要研究方向岩溶水文地质、环境地质。E-mail：28409807@qq.com

中图分类号: U453.6
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- 被引次数: 0
出版历程
- 收稿日期: 2022-05-20
- 网络出版日期: 2023-12-28
- 刊出日期: 2023-12-01

Application of different time series models to the prediction for mine water inflow in karst mountainous areas

1.
Guizhou Geological Environment Monitoring Institute, Guiyang, Guizhou 550081, China
2.
College of Resources and Environmental Engineering, Guizhou University, Guiyang, Guizhou 550025, China

摘要

摘要: 矿井涌水量预测的精度对于煤矿开采安全有着至关重要的作用。文章以老鹰山煤矿为例，分析降雨与矿井涌水量的相关关系，结果表明：同期月及前第1个月降雨量与涌水量相关性具有逐渐减弱的趋势，而与前第2个月至第5个月的相关性有逐渐升高的趋势；基于矿井涌水量及降雨量，建立了单因素季节性时间序列SARIMA模型及多元季节性时间序列SARIMAX模型对矿井涌水量进行预测，预测结果表明：两种模型91.7%的预测值达到B级探明的矿井涌水量，预测精度均较高，SARIMAX模型预测结果的MAPE为18.57%，小于SARIMA模型的25.27%，预测精度更优。
- 岩溶山区 /
- 矿井涌水量 /
- 预测 /
- SARIMA模型 /
- SARIMAX模型
Abstract: Coal resources are one of the important mineral resources in China. In the process of coal mining, due to the complex hydrogeological conditions in the mining area, and ineffective water exploration and discharge, accidents of mine water inrush occasionally occur, which may seriously restrict the safe production of coal resources. According to statistics, from 2000 to 2017, there were 1,173 accidents of coal mine flood in China, with 4,760 deaths. Therefore, the prediction reliability of mine water inflow plays a vital role in the safety of coal mining. A time series model is specifically designed to simulate and predict a time-sequential, time-varying, and interrelated data series. Most time series models require that the data must be stationary and the time series must follow a normal distribution. Taking Laoyingshan coal mine as an example, this study establishes a model of Seasonal Auto-Regressive Integrated Moving Average (SARIMAX model) and a model of Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors (SARIMA model), compares the fitting and prediction results of these two models, and evaluates their adaptability in prediction of mine water inflow in karst mountainous areas. Based on the monthly average rainfall and monthly average water inflow from October 1994 to December 2014, a SARIMA model for univariate seasonal time series and a SARIMAX model for multivariate seasonal time series have been established. To establish a corresponding mathematical model, it is necessary to perform a parameter significance test on each model, analyze the model fitting goodness and model fitting accuracy, and determine the optimal model. The test parameters can be selected from the coefficient of determination R2 of the sample, the Nash efficiency coefficient (NSE), the mean absolute percentage error (MAPE), the deviation, the root mean square error (RMSE), the AIC value, the BIC value and other indicators to test. Since NSE, RMSE, R2, and MAPE standards are correlated in some degree, the NSE, AIC and BIC values are selected as the criteria for validating the quality of the model. The above two different models are used to predict the average monthly water inflow of the mine in 2015. The model prediction results show that, except for the SARIMA model in November 2015 and the SARIMAX model in July 2015, the MAPE is greater than 40%. According to Qian Xuepu's classification of the prediction accuracy of mine water inflow, these prediction results can reach the mine water inflow of Level B. According to the relative error of the prediction results, the MAPE errors of the SARIMA model in the first 4 months and those of the SARIMAX model in the first 5 months are both within 25%, and the subsequent errors experience a maximum value or a large fluctuation with the step size, indicating good short-term prediction but poor adaptability for long-term prediction of these two models. Even so their prediction accuracy can still reach the mine water inflow controlled by Level C. In terms of the prediction accuracy, the SARIMAX model is more accurate in prediction than the SARIMA model. The main reason is that the SARIMA model is a univariate prediction model, which predicts the later changes only based on the time series changes of the water inflow itself, but ignores the external factors caused by the water inflow. The SARIMAX model only introduces the influence of rainfall on water inflow, but as one of the important factors affecting water inflow, rainfall plays an obvious role in improving the prediction accuracy. The correlation between rainfall and mine water inflow indicates that atmospheric precipitation is the main source for water recharge, and mining fissures are the main recharges channels in the mining area. The change of water inflow has a certain hysteresis effect relative to rainfall. With the extension of mining level, the increase of the mining area and the backfilling of the water-conducting fissures caused by the goaf collapse, the hysteresis effect of rainfall becomes increasingly obvious. The correlation between rainfall and inflow in the same month and the first previous month radually decreases, while it gradually increases from the second and fifth months. Based on the mine water inflow and rainfall, the SARIMA model for univariate seasonal time series and the SARIMAX model for multivariate seasonal time series have been established to predict the mine water inflow. The prediction results show that 91.7% of the predicted values of the two models reach the mine water inflow of Level B, and the prediction accuracy is high. The MAPE of SARIMAX model is 18.57%, less than that of SARIMA model (25.27%), indicating higher accuracy of SARIMAX model.
- karst mountainous area /
- mine water inflow /
- prediction /
- the SARIMA model /
- the SARIMAX model

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图 1 研究区环境地质简图

Figure 1. Environmental geology of the study area

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图 2 研究区剖面图

Figure 2. Section of the study area

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图 3 月平均降雨量及月平均涌水量时序图

Figure 3. Time sequence diagram of average monthly rainfall and average monthly water inflow

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图 4 同期月及前4月月平均降雨量与月平均涌水量相关关系图

Figure 4. Correlation between average monthly rainfall and average monthly water inflow in the same month and the first 4 months

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图 5 不同时段同期月及前4月月平均降雨量与月平均涌水量相关关系变化趋势图

注：横坐标1代表1994—2015年降雨量与涌水量之间的相关关系，2代表1995—2015年降雨量与涌水量之间的相关关系，依次类推，19代表2012—2015年降雨量与涌水量之间的相关关系

Figure 5. Change trend of the correlation between the average monthly rainfall and the average monthly water inflow in the same period and the first 4 months in different periods

Note: Abscissa 1 represents the correlation between precipitation and water inflow from 1994 to 2015. Abscissa 2 represents the correlation between precipitation and water inflow from 1995 to 2015. Successively, abscissa 19 represents the correlation between precipitation and water inflow from 2012 to 2015.

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图 6 涌水量自相关及偏自相关函数图

Figure 6. Auto-correlation and partial auto-correlation function of water inflow

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图 7 SARIMA模型及SARIMAX模型拟合结果图

Figure 7. Fitting result of the SARIMA model and the SARIMAX model

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图 8 残差序列相关函数图

Figure 8. Correlation function chart of residual sequence

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表 1 序列ADF检验结果表

Table 1. Results of sequence ADF test

ADF检验统计量		原始涌水量Q序列
		t-Statistic	Prob.
		−9.324761	0.0000
检验界值	1% level	−3.456408
	5% level	−2.872904
	10% level	−2.572900

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表 2 不同模型下的标准 BIC 、AIC 、NSE及 MAPE 值

Table 2. Standard BIC, AIC, NSE and MAPE values under different models

Model（p，d，q）（P，D，Q）^S	BIC	AIC	NSE	MAPE/%
SARIMA（3，0，0）（1，0，1）¹²	2.8805	2.8593	0.8291	16.74
SARIMA（3，0，0）（1，0，0）¹²	2.9614	2.9438	0.7591	18.74
SARIMA（2，0，0）（1，0，1）¹²	2.8802	2.8626	0.8255	17.29
SARIMA（2，0，0）（1，0，0）¹²	2.9625	2.9484	0.7528	18.90
SARIMAX（3，0，0）（1，0，1）¹²	2.6747	2.6435	0.8627	17.85
SARIMAX（3，0，0）（1，0，0）¹²	2.6693	2.6416	0.8626	17.88
SARIMAX（2，0，0）（1，0，1）¹²	2.6814	2.6537	0.8555	18.42
SARIMAX（2，0，0）（1，0，0）¹²	2.6768	2.6526	0.8549	18.55

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表 3 模型参数估计

Table 3. Estimation of model parameters

模型	参数	参数估计值	标准误差	T	显著性
SARIMA(3, 0, 0)(1, 0, 1)¹²	AR{1}	0.8504	0.0452	18.8302	0
	AR{2}	−0.3628	0.0676	−5.3686	0
	AR{3}	0.1456	0.0625	2.3285	0.02
	SAR{1}	0.9655	0.0070	137.3414	0
	SMA{1}	−0.7492	0.0367	−20.4154	0
SARIMAX(3, 0, 0)(1, 0, 0)¹²	AR{1}	0.7389	0.0498	14.8260	0
	AR{2}	−0.0904	0.0382	−2.3698	0.02
	AR{3}	0.2206	0.0389	5.6650	0
	SAR{1}	0.4438	0.0462	9.5986	0
	Beta(P)	0.4131	0.0537	7.6868	0
	Beta(P1)	−0.2044	0.0617	−3.3120	0
	Beta(P2)	0.7389	0.0498	14.8260	0

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表 4 2015年涌水量预测值

Table 4. Prediction value of water inflow in 2015

预测时段	实测及预测流量/m³·h⁻¹			MAPE/%
预测时段	实测	SARIMA模型	SARIMAX模型	SARIMA模型	SARIMAX模型
2015年1月	143.0	150.9	156.2	5.51	9.22
2015年2月	137.6	119.5	125.0	13.15	9.16
2015年3月	125.8	100.0	131.6	20.53	4.59
2015年4月	119.9	98.5	148.3	17.86	23.72
2015年5月	150.3	103.0	139.3	31.46	7.30
2015年6月	185.3	161.5	240.3	12.82	29.68
2015年7月	251.4	339.7	387.4	35.14	54.10
2015年8月	292.4	398.8	384.5	36.38	31.50
2015年9月	362.2	318.2	379.5	12.14	4.78
2015年10月	382.0	247.8	365.5	35.14	4.32
2015年11月	347.2	180.9	258.1	47.90	25.65
2015年12月	219.0	141.9	177.7	35.22	18.85

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