大坝位移性态的多模型联合预警方法

姜振翔; 陈辉; 陈鲁皖

doi:10.13203/j.whugis20210321

大坝位移性态的多模型联合预警方法

1.
南昌工程学院水利与生态工程学院,江西南昌,330099

基金项目:

国家自然科学基金 52109156

江西省教育厅科学技术研究项目 GJJ190970

详细信息

作者简介:
姜振翔,博士,讲师,主要从事大坝安全监控与健康诊断工作。jiangzhenxiang89@163.com

中图分类号: P258;TV698.1
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出版历程
- 收稿日期: 2021-06-14
- 网络出版日期: 2022-10-20
- 刊出日期: 2024-02-04

A Multi‑model Early Warning Method for Dam Displacement Behavior

School of Hydraulic & Ecological Engineering,Nanchang Institute of Technology, Nanchang330099, China

摘要

摘要:
传统方法采用单一的模型开展大坝位移性态预警,虚假警报频次较高。为提升预警结果的可靠性,提出多模型联合预警方法。以水位-温度-时效模型(hydraulic-season-time, HST)、自回归滑动平均模型(autoregressive moving aver‍age, ARMA)为研究对象,采用核密度估计探讨了两类模型残差的一维分布规律。在此基础上,对两类模型的联合残差进行了频率分析,发现了联合残差非尾部弱相关、尾部强相关的分布特征。采用Copula函数对HST-ARMA联合残差进行拟合,得到了联合分布函数,实现了大坝位移性态的多模型联合预警。算例表明,采用单一的HST模型或ARMA模型预警,受建模序列特征以及模型结构特征的影响,虚假警报发生率高达23.17%~27.94%。而采用HST-ARMA联合预警,能够充分结合各模型的优势,虚假警报发生率可降至0.00%~0.63%。多模型联合预警能够有效降低虚假警报的发生频次,预警结果能够更加真实地反映大坝位移性态,可为提升大坝安全管理水平提供参考。
- 大坝位移 /
- 监控模型 /
- 分布分析 /
- 连接函数 /
- 联合预警
Abstract:
Objectives
The traditional method uses a single monitoring model to conduct the early warning of dam displacement behavior. However, the single monitoring model may not reflect the real behavior of the dam due to its low accuracy, thus causing false alarms.
Methods
In order to improve the reliability of early warn‍ing results, a new multi-model early warning method is proposed. The hydraulic-season-time (HST) model and autoregressive moving average (ARMA) model, which are the most common models in engineering, are taken as the basic model. First, the advantages and disadvantages of the two models in dealing with dam displacement monitoring data are analyzed. Then the one-dimensional residual distribution of the two models is discussed by kernel density estimation. On this basis, the frequency analysis of the joint residuals of HST-ARMA is carried out and it shows the joint residuals is weakly correlated in non-tail, but strongly correlated in tail. Finally, the Copula function is used to fit the joint residuals of HST-ARMA, and the joint distribution function is obtained, which realizes the joint early warning of dam displacement behavior with multiple models.
Results
It is verified by several measuring points on the wire alignment system of concrete dam. The case study shows that if a single HST model or ARMA model is used for early warning, the false alarm rate can reach 23.17%-27.94% due to the influence of modeling sequence features and model structure features. And if the HST-ARMA method is used, the false alarm rate can be reduced to 0.00%‍‍‍‍-0.63% due to combine the advantages of different models.
Conclusions
The new method can combine the advantag‍es of different models and avoid the disadvantages of the single model, thus effectively reducing the frequency of false alarms. The warning results of HST-ARMA method are more reliable and can more truly reflect the dam displacement behavior. It can provide reference for improving the dam safety management level.
- dam displacement /
- monitoring model /
- distribution analysis /
- Copula function /
- joint warning
http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20210321

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http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20210321

图 1 单模型预警方法与多模型联合预警方法

Figure 1. Single Model Early Warning Method and Multi-model Joint Early Warning Method

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图 2 HST‐ARMA联合预警方法流程图

Figure 2. Flowchart of HST‐ARMA Joint Early Warning Method

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图 3 过程线与趋势线

Figure 3. Process Lines and Trend Lines

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图 4 各测点预报期残差过程线

Figure 4. Process Lines of Residual Errors in Forecast Periods

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图 5 各测点HST模型与ARMA模型残差分布

Figure 5. Residual Distribution of HST Model and ARMA Model at Each Measurement Point

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图 6 各测点联合残差二维频率直方图和Copula密度函数图

Figure 6. Two‑Dimensional Frequency Histogram and Copula Density Function Diagram of Residual Errors at Each Measuring Point

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图 7 HST‑ARMA联合预警成果

Figure 7. HST‑ARMA Joint Monitoring Results

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表 1 单模型预警指标与多模型联合预警指标

Table 1 Index of Single Model Early Warning Method and Multi-model Joint Early Warning Method

预警方法	预警指标	正常	预警	异常
单模型预警	$Δ_{1}$	$[- 2 S_{1}, 2 S_{1}]$	$[- 3 S_{1}, - 2 S_{1}) ⋃ (2 S_{1}, 3 S_{1}]$	$(- \infty, - 3 S_{1}) ⋃ (3 S_{1}, + \infty)$
单模型预警	$Δ_{2}$	$[- 2 S_{2}, 2 S_{2}]$	$[- 3 S_{2}, - 2 S_{2}) ⋃ (2 S_{2}, 3 S_{2}]$	$(- \infty, - 3 S_{2}) ⋃ (3 S_{2}, + \infty)$
多模型联合预警	$(F_{H S T} (Δ_{1}), F_{A R M A} (Δ_{2}))$	位于区域③	位于区域②	位于区域①
概率 $P$ /%		95.46	4.27	0.27

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表 2 HST模型参数

Table 2 HST Model Parameters

测点	参数
测点	$a_{0}$	$a_{1}$	$a_{2}$	$a_{3} / 10^{- 4}$	$b_{1}$	$b_{2}$	$b_{3}$	$b_{4}$	$b_{5}$	$c_{1}$	$c_{2}$
EX421	71.211	-0.022	-0.323	1.660	-0.033	0.014	-0.075	-0.091	-0.127	-0.439	1.258
EX423	7.883	-	-	-	-0.034	0.050	-0.059	-0.201	-0.128	-0.401	0.827
EX424	96.232	-1.629	-	0.532	-0.039	0.035	-0.079	-0.145	-0.151	-0.388	1.351
EX425	154.376	-2.412	-	1.112	-0.035	-	-0.055	-0.133	-0.138	-0.213	-

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表 3 ARMA模型参数

Table 3 ARMA Model Parameters

测点	$δ_{t - 1}$	$δ_{t - 2}$	$δ_{t - 3}$	$δ_{t - 4}$	$δ_{t - 5}$
EX421	0.889	0.069	-0.038	0.022	0.036
EX423	0.892	0.058	0.039	0.007	-
EX424	0.926	0.064	0.011	-	-
EX425	0.837	0.129	0.007	-	-

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表 4 建模期拟合精度评价指标

Table 4 Evaluation Indexes of Fitting Accuracy in the Modeling Period

误差指标	模型	测点
误差指标	模型	EX421	EX423	EX424	EX425
R	HST	0.90	0.89	0.91	0.91
R	ARMA	0.93	0.91	0.92	0.94
S	HST	1.50	1.22	1.20	1.25
S	ARMA	1.23	1.26	1.25	1.27

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表 5 HST模型预报期警报率统计

Table 5 Statistics of Early Warning Rate of HST Model in the Forecast Period

测点	正常次数	轻度异常次数	异常次数	次数合计	轻度异常率/%	异常率/%	总警报率/%
EX421	230	64	21	315	20.32	6.67	26.98
EX423	229	61	25	315	19.37	7.94	27.30
EX424	227	65	23	315	20.63	7.30	27.94
EX425	229	63	23	315	20.00	7.30	27.30

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表 6 ARMA模型预报期警报率统计

Table 6 Statistics of Early Warning Rate of ARMA Model in the Forecast Period

测点	正常次数	轻度异常次数	异常次数	次数合计	轻度异常率/%	异常率/%	总警报率/%
EX421	242	54	19	315	17.14	6.03	23.17
EX423	235	60	20	315	19.05	6.35	25.40
EX424	240	57	18	315	18.10	5.71	23.81
EX425	232	63	20	315	20.00	6.35	26.35

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表 7 预报期HST模型与ARMA模型联合预警结果

Table 7 Joint Monitoring Results of HST Model and ARMA Model in the Forecast Period

测点	正常次数	轻度异常次数	异常次数	次数合计	轻度异常率/%	异常率/%	总警报率/%
EX421	314	1	0	315	0.32	0	0.32
EX423	315	0	0	315	0.00	0	0.00
EX424	313	2	0	315	0.63	0	0.63
EX425	313	2	0	315	0.63	0	0.63

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