﻿ 局部变权和云理论在悬索桥综合评估中的应用
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 浙江大学学报(工学版)  2017, Vol. 51 Issue (8): 1544-1550  DOI:10.3785/j.issn.1008-973X.2017.08.009 0

### 引用本文 [复制中英文]

dx.doi.org/10.3785/j.issn.1008-973X.2017.08.009
[复制中文]
XU Xiang, HUANG Qiao, REN Yuan. Local variable weight and cloud theory applied in suspension bridge comprehensive assessment[J]. Journal of Zhejiang University(Engineering Science), 2017, 51(8): 1544-1550.
dx.doi.org/10.3785/j.issn.1008-973X.2017.08.009
[复制英文]

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orcid.org/0000-0003-1167-3588.
Email: qhuanghit@126.com

### 文章历史

Local variable weight and cloud theory applied in suspension bridge comprehensive assessment
XU Xiang , HUANG Qiao , REN Yuan
School of Transportation, Southeast University, Nanjing 210096, China
Abstract: A bridge assessment approach was proposed based on the local variable weight principle and the cloud theory in order to overcome the disadvantages of the constant weight comprehensive assessment and the fuzzy assessment methods. The local variable weight model was established according to the analysis of the variable-weight character in bridge assessment. The parameters of the local variable weight model were determined based on the assessment instances. The effective domain of normal cloud model was decided by the current codes. Mathematical expectation, entropy and hyper entropy were calculated based on the effective domain. The normal cloud chart was generated by the forward cloud transformation. A suspension bridge was taken as an example to prove the feasibility and practicability of the proposed method. The results of the proposed method accorded with the actual maintenance strategy.
Key words: suspension bridge    bridge assessment    local variable weight    cloud theory    normal cloud model

1 局部变权原理

1) $\sum\limits_{j = 1}^m {{W_j}} \left( X \right) = 1$

2) 对任意的j∈{1, 2, …, m}, 均存在Tj, Uj∈(0, 1), 且TjUj, 使得Wj(X)关于xj在[0, Tj]上单调递减, 而在[Uj, 1]上单调递增；

1) ${W_j}\left( X \right) = \frac{{W_i^0{S_i}\left( X \right)}}{{\sum\limits_{k = 1}^m {W_k^0{S_k}\left( X \right)} }}$关于xj在[0, Tj]上单调递减, 而在[Uj, 1]上单调递增；

2) xkxiTkTiSk(X)≥Si(X), UkUixkxiSk(X)≤Si(X)；

2 云理论简介 2.1 云理论的基本概念

U为一个论域, CU上的模糊集合, 对于任意的元素xC的隶属度是有稳定倾向的随机数μ(x), 则隶属度在U上的分布称为隶属云, 记为云C(x), (x, μ(x))称为云滴.

2.2 正态云模型

 ${E_x}_i = {c_{i{\rm{min}}}} + {\theta _i}\left( {{c_{i{\rm{max}}}} - {c_{i{\rm{min}}}}} \right).$ (1)

 $3{\varepsilon _1}E_{{n_i}}^\prime = {\rm{max}}\left( {{c_{i{\rm{max}}}} - {E_{{x_i}}},{E_{{x_i}}} - {c_{i{\rm{min}}}}} \right).$ (2)

 $3{\varepsilon _2}{H_{{e_i}}} = {\rm{max}}\left( {E_{{n_i}}^\prime - {E_{{n_i}}},{E_{{n_i}}} - E_{{n_i}}^\prime } \right).$ (3)

 图 1 FCT生成正态云图的流程框图 Fig. 1 Flow chart for normal cloud model generation by FCT
3 悬索桥综合技术状况评估 3.1 评估模型与指标权重

《公路桥涵养护规范》(JTG H11-2004) 和《公路桥梁技术状况评定标准》(JTG/T H21-2011) 为了满足评估对象的普遍适用性, 将桥梁结构划分为上部结构、下部结构和桥面系.但是, 大跨径悬索桥结构形式复杂, 规范的结构划分层次适用性不强, 需要更加精细的层次划分.本文根据大跨径悬索桥的结构层次特点, 综合考虑安全性、耐久性和适用性, 以全面性、简捷性、独立性、客观性和可检性为指标选取原则, 融合人工检查、健康监测和无损检测数据, 建立基于多源数据的综合技术状况评估模型.该评估模型以主缆系统、吊索系统、加劲梁、索塔、锚碇、下部结构和附属设施为一级指标；选择主缆索股索力、主缆线形和主缆索体等31个元素为二级指标.大跨悬索桥综合技术状况评估模型中的具体指标如图 2所示.

 图 2 悬索桥综合技术状况评估模型 Fig. 2 Comprehensive technical condition assessment model for suspension bridges

3.2 确定局部变权模式

 ${S_j}\left( X \right) = \left\{ {\begin{array}{*{20}{l}} {{\rm{exp}}({p_1}\left( {100 - {x_j}} \right)) + c - 1,{\rm{ }}} & {x \in \left[ {{U_1},100} \right];}\\ {{\rm{exp}}({p_2}\left( {{U_1} - {x_j}} \right)) + {\rm{exp}}({p_1}\left( {100 - {U_1}} \right)) + c - 2,} & {x \in \left[ {{U_2},\left. {{U_1}} \right)} \right.;}\\ {{\rm{exp}}({p_3}\left( {{U_2} - {x_j}} \right)) + {\rm{exp}}({p_2}\left( {{U_1} - {U_2}} \right)) + {\rm{exp}}({p_1}\left( {100 - {U_1}} \right)) + c - 3,} & {x \in \left[ {{U_3},\left. {{U_2}} \right)} \right.;}\\ {{\rm{exp}}({p_4}\left( {{U_3} - {x_j}} \right)) + {\rm{exp}}({p_3}\left( {{U_2} - {U_3}} \right)) + } & {}\\ {{\rm{exp}}({p_2}\left( {{U_1} - {U_2}} \right)) + {\rm{exp}}({p_1}\left( {100 - {U_1}} \right)) + c - 4,} & {x \in \left[ {{U_4},\left. {{U_3}} \right)} \right.;}\\ {{\rm{exp}}({p_5}\left( {{U_4} - {x_j}} \right)) + {\rm{exp}}({p_4}\left( {{U_3} - {U_4}} \right)) + {\rm{exp}}({p_3}\left( {{U_2} - {U_3}} \right)) + } & {}\\ {\quad \quad {\rm{exp}}({p_2}\left( {{U_1} - {U_2}} \right)) + {\rm{exp}}({p_1}\left( {100 - {U_1}} \right)) + c - 5,} & {x \in \left[ {0,\left. {{U_4}} \right).} \right.} \end{array}} \right.$ (4)

3.3 局部变权模型参数验证

《公路桥涵养护规范》(JTG H11-2004) 中规定, 桥梁评估结果可以用于指导养护维修策略的制定, 具体对应关系如表 2所示.

3.4 确定正态云模型参数

 图 3 正态云模型 Fig. 3 Normal cloud model
3.5 评估示例

4 结论

(1) 提出了适用于悬索桥评估的局部变权模式.本文选择指数型状态变权向量对应的变权模式作为研究对象, 根据现行行业规范《公路桥梁技术状况评定标准》(JTG/T H21-2011) 将指标评分值分为5个部分, 根据试算分别确定了5个部分的惩罚水平(p1, p2, p3, p4, p5)和变权幅度c等参数的取值, 使得各阶段变权效果和桥梁劣化规律相一致.

(2) 建立了适用于桥梁评估研究的正态云模型.本文根据现行行业规范确定了云模型的有效论域, 并根据有效论域确定了云模型中3个参数ExEnHe的取值, 利用前向云发生器建立了正态云模型.云理论有效地解决了模糊评估方法中隶属度函数难以确定的问题, 将对象的模糊性和随机性进行了有效融合.

(3) 通过算例分析验证了本文提出方法的可行性和适用性.采用本文提出的评估方法对某悬索桥进行评估计算, 对评估结果进行分析发现, 本文提出的评估方法得到的评估结果与实际维修对策相符, 且评估结果能够体现模糊性和随机性.

 [1] HUANG Q, REN Y, LIN Y. Application of uncertain type of AHP to condition assessment of cable-stayed bridges[J]. Journal of Southeast University:English Edition, 2007, 23(4): 599–603. [2] SAATY T. Analytic hierarchy process[M]//Wiley StatsRef:Statistics Reference Online. John Wiley & Sons, Ltd, 2014:15-45. [3] JIAO Y, LIU H, CHENG Y, et al. Fuzzy neural network-based damage assessment of bridge under temperature effect[J]. Mathematical Problems in Engineering, 2014, 2014(1): 1–9. [4] 兰海, 史家钧. 灰色关联分析与变权综合法在桥梁评估中的应用[J]. 同济大学学报:自然科学版, 2001, 29(1): 50–54. LAN Hai, SHI Jia-jun. Degree of grey incidence and variable weight synthesizing applied in bridge assessment[J]. Journal of Tongji University:Natural Science Edition, 2001, 29(1): 50–54. [5] SASMAL S, RAMANJANEYULU K. Condition evaluation of existing reinforced concrete bridges using fuzzy based analytic hierarchy approach[J]. Expert Systems with Applications, 2008, 35(3): 1430–1443. DOI:10.1016/j.eswa.2007.08.017 [6] 任远. 大跨度斜拉桥养护管理系统的数字化研究[D]. 哈尔滨: 哈尔滨工业大学, 2008. REN Yuan. Digitization research on maintenance and management system of long-span cable-stayed bridges[D]. Harbin:Harbin Institute of Technology, 2008. http://cdmd.cnki.com.cn/Article/CDMD-10213-2009223796.htm [7] 汪培庄. 模糊集与随机集落影[M]. 北京: 北京师范大学出版社, 1985: 10-13. [8] 李洪兴. 因素空间理论与知识表示的数学框架(Ⅷ):变权综合原理[J]. 模糊系统与数学, 1995(3): 1–9. LI Hong-xing. Factor spaces and mathematical frame of knowledge representation(Ⅷ):varied weight principle[J]. Fuzzy Systems and Mathematics, 1995(3): 1–9. [9] 姚炳学, 李洪兴. 局部变权的公理体系[J]. 系统工程理论与实践, 2000, 20(1): 106–109. YAO B, LI H. Axiomatic system of local variable weight[J]. System Engineering Theory & Practice, 2000, 20(1): 106–109. [10] WU Q, LI B, CHEN Y. Vulnerability assessment of groundwater inrush from underlying aquifers based on variable weight model and its application[J]. Water Resources Management, 2016, 30(10): 3331–3345. DOI:10.1007/s11269-016-1352-4 [11] CHEN Z, ZHANG H, HAN D. Research on comprehensive performance assessment for wsn based on anp with equilibrium variable weight and cloud gravity center[J]. China Communications, 2015(S2): 1–9. [12] 李德毅, 孟海军, 史雪梅. 隶属云和隶属云发生器[J]. 计算机研究与发展, 1995, 32(6): 15–20. LI Di-yi, MENG Hai-jun, SHI Xue-mei. Membership clouds and membership cloud cenerators[J]. Journal of Computer Research and Development, 1995, 32(6): 15–20. [13] 李德毅, 刘常昱. 论正态云模型的普适性[J]. 中国工程科学, 2004, 6(8): 28–34. LI De-yi, LIU Chang-. yu Study on the university of the noamal cloud model[J]. Chinese Engineering Science, 2004, 6(8): 28–34. [14] WANG G, XU C, LI D. Generic normal cloud model[J]. Information Sciences, 2014, 280(280): 1–15. [15] DONG W, ZENG D, SINGH V P, et al. A cloud model-based approach for water quality assessment[J]. Environmental Research, 2016(149): 113–121. [16] YANG J, LIU H, YU X, et al. Entropy-cloud model of heavy metals pollution assessment in farmland soils of mining areas[J]. Polish Journal of Environmental Studies, 2016, 25(3): 1315–1322. DOI:10.15244/pjoes/61883 [17] 杨宝臣, 陈跃. 基于变权和TOPSIS方法的灰色关联决策模型[J]. 系统工程, 2011(6): 106–112. YANG Bo-chen, CHEN Yue. Grey relational decision-making model based on variable weight and TOPSIS method[J]. System Engineering, 2011(6): 106–112.