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Determination of monitoring index for concrete dam based on improved POT model
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摘要: 大坝监测效应量作为一种随机变量，采用以极值理论为基础的POT (Peaks over Threshold)模型研究监测效应量的监控指标是合适的，但现有的POT模型的阈值确定以图形法为主，需要人工判断，主观性和随意性较大，且难以实现计算机自动化识别。通过构建阈值递增序列，计算不同阈值
$ {T}_{j} $ 条件下相应的监控指标，然后利用概率论中的3σ准则，以监控指标危险值与警戒值的差值$ {\Delta }_{j} $ 趋近于测值序列标准差S作为确定最合理阈值的原则，提出了一种改进的阈值确定方法，并给出了一个验证实例。改进方法理论基础明确，有效地克服了图形法的主观性和随机误差，且能采用计算机程序实现最合理阈值的自动识别，增强了POT模型法拟定大坝安全监控指标的实用性。-
关键词:
- 监控指标 /
- POT模型 /
- 阈值 /
- 广义Pareto分布 /
- 3σ准则
Abstract: As the dam monitoring effect quantity is a random variable, the peaks over threshold (POT) model based on the extreme value theory can be adopted to study the monitoring index of the monitoring effect quantity. However, the threshold in the existing POT model is usually determined by graphic methods, which require human judgment and lead to strong subjectivity and randomness, and automatic computer identification is difficult to realize. In this study, a threshold increment sequence is constructed and the corresponding monitoring indexes under different thresholds are calculated. An improved threshold determination method is then developed based on the "3σ criterion" in probability theory, in which the most reasonable threshold is selected while the difference between the dangerous value and the warning value of the monitoring index approaches to the standard deviation of the measured value sequence. Verification example shows that the improved method is of a clear theoretical foundation and effectively reduces the subjectivity and random errors of the graphical methods. By using computer programs, automatic recognition of the most reasonable threshold can be realized, which enhances the practicability of the POT model in determination of the dam safety monitoring index.-
Key words:
- monitoring index /
- POT model /
- threshold /
- generalized Pareto distribution /
- 3σ criterion
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图 1 EX406测点实测水平位移及相应环境量变化过程线
Figure 1. Process lines of measured horizontal displacement for EX406 measuring point and corresponding environmental quantity
表 1 EX406测点POT模型计算参数
Table 1. Calculation parameters of EX406 measuring point in POT model
项目 样本数 ${T_j}$/mm ${\xi _{{T_j}}}$ ${\sigma _{{T_j}}}$ ${c_j} = \left. {\left| {{\Delta _j} - S} \right.} \right|$ 下游方向 137 4.64 0.03 0.54 0.02 上游方向 99 2.64 0.06 0.68 0.03 
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