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摘要: 現有的大壩整體性態評價方法以定性評價為主，主觀性較強。針對這一問題，以單測點監控模型的計算值與監測儀器實測值之間的殘差為基礎，提出采用多測點融合殘差表征大壩整體性態。結合信息熵理論研究了不同測點的殘差變化規律，從而對各測點殘差的融合權重進行了分配，計算了融合殘差。通過對融合殘差進行分布分析，利用逆向云發生器、正向云發生器建立了表征大壩不同性態的概念云，即評價標準。在此基礎上，結合云相似度算法，建立了大壩整體性態的評價模型。算例表明，該模型能夠有效識別大壩監測資料中的異常測值，并能夠定量、客觀地評價大壩整體性態，評價結果合理、可靠，可為保障大壩安全運行提供重要參考。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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圖 2 不同相交條件下的云重疊面積。（a）全云Cq與Cl相交，一個交點；（b）全云Cq與Cl相交，兩個交點；（c）半云Cq與Cl相交，一個交點；（d）半云Cq與Cl相交，兩個交點
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
圖 3
$ {\boldsymbol{\varDelta}} $ 概率密度曲線及下分位點位置示意Figure 3. Probability density curve of
$ {\boldsymbol{\varDelta}} $ and the fractile
圖 4 混凝土壩監測信息。（a）壩頂引張線示意圖；（b）EX401~EX409測點過程線；（c）上游水位與溫度過程線
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
圖 6 融合殘差特征。（a）融合殘差的概率密度曲線與特征分位點；（b）大壩整體性態評價標準（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)
圖 7 概念云與評價云(2010—2014年)外包絡曲線。（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 云重疊面積計算方法
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 大壩整體性態評價標準(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監控模型計算值與實測值相關系數
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 各測點殘差的權重
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 概念云特征參數
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年各年度云特征參數
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年各年評價云與概念云的相似度
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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