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摘要: 现有的大坝整体性态评价方法以定性评价为主，主观性较强。针对这一问题，以单测点监控模型的计算值与监测仪器实测值之间的残差为基础，提出采用多测点融合残差表征大坝整体性态。结合信息熵理论研究了不同测点的残差变化规律，从而对各测点残差的融合权重进行了分配，计算了融合残差。通过对融合残差进行分布分析，利用逆向云发生器、正向云发生器建立了表征大坝不同性态的概念云，即评价标准。在此基础上，结合云相似度算法，建立了大坝整体性态的评价模型。算例表明，该模型能够有效识别大坝监测资料中的异常测值，并能够定量、客观地评价大坝整体性态，评价结果合理、可靠，可为保障大坝安全运行提供重要参考。Abstract: A dam is an important piece of infrastructure for ensuring economic and social development. During operation, because of environmental changes, aging materials, and other factors, a dam may develop accident risks and once it fails, it poses a great threat to society. Therefore, it is of great significance to use reasonable methods for analyzing the monitoring data collected by a dam safety monitoring system and evaluate a dam’s behavior to ensure operation safety. At present, the existing methods are mainly devoted to evaluating the local state of a dam according to the monitoring information of a single measuring point. Relatively few studies are available on the evaluation methods for the overall state of a dam, and the existing methods are mainly qualitative and subjective. To address this problem, the residual between the model calculated value and the measured value was taken as the research basis. The concept of the fusion residual, an important index for characterizing the overall behavior of a dam, was promoted. Combined with the information entropy theory, the variation of residuals at different measuring points was studied, and the fusion weight of residuals at each measuring point was analyzed. The fusion residual was calculated. Based on the distribution analysis of the fusion residual, a concept cloud representing the different states of a dam, namely, the evaluation criteria, was established using a reverse cloud generator and a forward cloud generator. On this basis, an evaluation model of the overall behavior of a dam was established and combined with the cloud similarity algorithm. The example shows that the evaluation method can effectively identify the abnormal value of a dam and evaluate its overall behavior. The evaluation results are reasonable and reliable. The model can evaluate the overall behavior of a dam quantitatively and objectively, and the evaluation results are reasonable and reliable, providing an important reference for the safe operation of a dam.
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Key words:
- dam /
- fusion residual /
- overall behavior /
- cloud theory /
- evaluation model
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图 2 不同相交条件下的云重叠面积。（a）全云Cq与Cl相交，一个交点；（b）全云Cq与Cl相交，两个交点；（c）半云Cq与Cl相交，一个交点；（d）半云Cq与Cl相交，两个交点
Figure 2. Overlapping area of clouds under different intersection conditions: (a) entire cloud Cq intersecting Cl with one intersection; (b) entire cloud Cq intersecting Cl with two intersections; (c) half cloud Cq intersecting Cl with one intersection; (d) half cloud Cq intersecting Cl with two intersections
图 3
$ {\boldsymbol{\varDelta}} $ 概率密度曲线及下分位点位置示意Figure 3. Probability density curve of
$ {\boldsymbol{\varDelta}} $ and the fractile
图 4 混凝土坝监测信息。（a）坝顶引张线示意图；（b）EX401~EX409测点过程线；（c）上游水位与温度过程线
Figure 4. Monitoring information of a concrete dam: (a) extension line in the dam crest; (b) process line of EX401‒EX409; (c) process line of the upstream water level and temperature
图 6 融合残差特征。（a）融合残差的概率密度曲线与特征分位点；（b）大坝整体性态评价标准（概念云）
Figure 6. Characteristics of fusion residuals: (a) probability density curve of fusion residuals and feature quantiles; (b) evaluation criteria for the integrity of a dam (conceptual cloud)
图 7 概念云与评价云(2010—2014年)外包络曲线。（a）2010年；（b）2011年；（c）2012年；（d）2013年；（e）2014年
Figure 7. Concept cloud and evaluation cloud envelope curve during year of 2010—2014: (a) 2010; (b) 2011; (c) 2012; (d) 2013; (e) 2014
表 1 云重叠面积计算方法
Table 1. Calculation method of the cloud overlapping area
Intersection diagram Abscissa of the intersection S Calculation method Fig.2(a) $ {x_{\text{a}}} $ $ {S_1} + {S_2} $ $ \int_{{E_{{\text{x,}}}}_l - 3{E_{{\text{n,}}}}_l}^{{x_{\text{a}}}} {{y_l}(x){\text{d}}x + \int_{{x_{\text{a}}}}^{{E_{{\text{x,}}q}} + 3{E_{{\text{n,}}q}}} {{y_q}(x){\text{d}}x} } $ Fig.2(b) $ {x_{\text{b}}},\;{x_{\text{c}}} $ $ {S_1} + {S_2} + {S_3} $ $ \int_{{E_{{\text{x,}}q}} - 3{E_{{\text{n,}}q}}}^{{x_{\text{b}}}} {{y_q}(x){\text{d}}x + \int_{{x_{\text{b}}}}^{{x_{\text{c}}}} {{y_l}(x){\text{d}}x} + \int_{{x_{\text{c}}}}^{{E_{{\text{x,}}q}} + 3{E_{{\text{n,}}q}}} {{y_q}(x){\text{d}}x} } $ Fig.2(c) $ {x_{\text{d}}} $ $ {S_1} + {S_2} $ $ \int_{{E_{{\text{x,}}l}} - 3{E_{{\text{n,}}l}}}^{{x_{\text{d}}}} {{y_l}(x){\text{d}}x + \int_{{x_d}}^{{E_{{\text{x,}}q}} + 3{E_{{\text{n,}}q}}} {{y_q}(x){\text{d}}x} } $ Fig.2(d) $ {x_{\text{e}}},\;{x_{\text{f}}} $ $ {S_1} + {S_2} + {S_3} $ $ \int_{{E_{{\text{x,}}q}} - 3{E_{{\text{n,}}q}}}^{{x_{\text{e}}}} {{y_q}(x){\text{d}}x + \int_{{x_{\text{e}}}}^{{x_{\text{f}}}} {{y_l}(x){\text{d}}x} + \int_{{x_{\text{f}}}}^{{E_{{\text{x,}}q}} + 3{E_{{\text{n,}}q}}} {{y_q}(x){\text{d}}x} } $ $ {S_q} $ — — $ \int_{{E_{{\text{x,}}q}} - 3{E_{{\text{n,}}q}}}^{{E_{{\text{x,}}q}} + 3{E_{{\text{n,}}q}}} {{y_q}(x){\text{d}}x} $ $ {S_l} $ — — $ \int_{{E_{{\text{x,}}l}} - 3{E_{{\text{n,}}l}}}^{{E_{{\text{x,}}l}} + 3{E_{{\text{n,}}l}}} {{y_l}(x){\text{d}}x} $ 
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表 2 大坝整体性态评价标准(概念云)
Table 2. Evaluation criteria for the integrity of a dam (conceptual cloud)
Concept cloud Qualitative concept Extraction range of cloud feature parameters ${C_1}$ Abnormal $( - \infty ,\;{\mu _{0.025}})$ ${C_2}$ Basically normal $[{\mu _{0.025}},\;{\mu _{0.150}})$ ${C_3}$ Normal $[{\mu _{0.150}},\;{\mu _{0.850}})$ ${C_4}$ Basically normal $[{\mu _{0.850}},\;{\mu _{0.975}})$ ${C_5}$ Abnormal $[{\mu _{0.975}},\; + \infty )$
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表 3 EX401~EX409监控模型计算值与实测值相关系数
Table 3. Correlation coefficient between the calculated value and measured value of EX401‒EX409
EX401 EX402 EX403 EX404 EX405 EX406 EX407 EX408 EX409 0.864 0.811 0.823 0.895 0.872 0.889 0.825 0.814 0.802
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表 4 各测点残差的权重
Table 4. Weight of residuals of each point
EX401 EX402 EX403 EX404 EX405 EX406 EX407 EX408 EX409 0.062 0.139 0.207 0.058 0.068 0.072 0.112 0.138 0.144
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表 5 概念云特征参数
Table 5. Characteristic parameters of the concept cloud
Concept cloud Qualitative concept Extraction range of cloud feature parameters Ex En He ${C_1}$ Abnormal $( - \infty ,\;{\mu _{0.025}})$ −1.6948 0.2755 0.0307 ${C_2}$ Basically normal $[{\mu _{0.025}},\;{\mu _{0.150}})$ −0.992 0.1867 0.0486 ${C_3}$ Normal $[{\mu _{0.150}},\;{\mu _{0.850}})$ −0.0171 0.407 0.1358 ${C_4}$ Basically normal $[{\mu _{0.850}},\;{\mu _{0.975}})$ 1.0776 0.247 0.0825 ${C_5}$ Abnormal $[{\mu _{0.975}},\; + \infty )$ 1.8814 0.2424 0.113
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表 6 2010—2014年各年度云特征参数
Table 6. Cloud parameters for each year from 2010—2014
Year ${E_{\text{x}}}$ ${E_{\text{n}}}$ ${H_{\text{e}}}$ 2010 −0.1326 0.6939 0.2186 2011 −0.2336 0.6308 0.1534 2012 0.0792 0.7781 0.2951 2013 −1.1044 0.4279 0.1125 2014 −0.2123 0.7098 0.2003
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表 7 2010—2014年各年评价云与概念云的相似度
Table 7. Similarity between evaluating clouds and concept clouds from 2010 to 2014
Year ${\eta _1}$ ${\eta _2}$ ${\eta _3}$ ${\eta _4}$ ${\eta _5}$ Evaluation results 2010 0.104 0.263 0.757 0.335 0.135 Normal 2011 0.108 0.302 0.896 0.283 0.109 Normal 2012 0.094 0.223 0.632 0.342 0.149 Normal 2013 0.196 0.499 0.384 0.049 0.016 Basically normal 2014 0.106 0.269 0.761 0.313 0.125 Normal
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