| 环境变化下基于核典型相关分析与协整的损伤识别方法 |
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| 引用本文： | 李东升,黄杰忠,李宏男.环境变化下基于核典型相关分析与协整的损伤识别方法[J].中国公路学报,2019,32(11):71-82. |
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| 作者姓名： | 李东升 黄杰忠 李宏男 |
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| 作者单位： | 1. 大连理工大学 建设工程学部, 辽宁 大连 116024;2. 汕头大学 广东省结构安全与监测工程技术研究中心, 广东 汕头 515063 |
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| 基金项目： | 国家重点基础研究发展计划（"九七三"计划）项目（2015CB057704）；国家自然科学基金项目（51578107，51778103，51121005）；中央高校基本科研业务费专项资金项目（DUT18LAB07）；汕头大学科研启动基金项目（NTF18012） |
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| 摘 要： | 采用传统协整方法进行损伤识别时，需要变量间满足较好的线性关系，而实际工程中监测变量往往存在一定程度的非线性，这使得协整方法的有效性受到影响。为此，提出一种结合核典型相关分析与协整的损伤识别方法。首先利用核典型相关分析能有效处理非线性相关变量的优点，将低维空间存在非线性关系的监测变量映射到高维空间，使其转化为线性相关的核典型变量。然后利用协整方法能够消除变量间共同趋势的特点，对核典型变量间的共同环境因素影响进行分离，并以分离环境因素影响后的协整残差作为损伤指标进行损伤识别。最后通过芬兰Kullaa课题组的木桁架桥试验数据，对协整方法、结合典型相关分析与协整的方法、核典型相关分析和协整相结合方法这3种方法的损伤识别结果进行比较。研究结果表明：在分析非线性数据方面，核典型相关分析要优于典型相关分析；前2种方法受监测变量数目的影响较大，选择不同数目的监测变量将得到不同的识别结果，而该方法对监测变量数目不敏感；且在损伤识别的漏判率方面该方法明显优于其他2种方法。
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| 关 键 词： | 桥梁工程 损伤识别 核典型相关分析 非线性相关 协整 环境因素影响 |
| 收稿时间： | 2018-09-15 |
Structural Damage Identification Based on Kernel Canonical Correlation Analysis and Cointegration Under Changing Environments |
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| LI Dong-sheng,HUANG Jie-zhong,LI Hong-nan.Structural Damage Identification Based on Kernel Canonical Correlation Analysis and Cointegration Under Changing Environments[J].China Journal of Highway and Transport,2019,32(11):71-82. |
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| Authors: | LI Dong-sheng HUANG Jie-zhong LI Hong-nan |
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| Affiliation: | 1. Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China;2. Guangdong Engineering Center for Structure Safety and Health Monitoring, Shantou University, Shantou 515063, Guangdong, China |
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| Abstract: | A cointegration-based method can be used for damage identification when the variables have a good linear relationship. However, in practical engineering, the relationship between the monitored variables is usually non-linear, which weakens the effectiveness of the cointegration method. This paper proposes a new method that combines kernel canonical correlation analysis with cointegration. Kernel canonical correlation analysis is a powerful technique for analyzing nonlinear correlation variables. A nonlinear transformation of monitored variables from the low-dimensional space to a high-dimensional space was performed through kernel canonical correlation analysis. The nonlinear monitored variables in low-dimensional space were thereby changed to linear kernel canonical variables in high-dimensional space. Because the cointegration method can remove the common trend among variables, cointegration was then applied to remove environmental influences in the kernel canonical variables. Damage can be identified by the change of cointegration residual. The numerical example shows that kernel canonical correlation analysis is more effective in processing nonlinear data than canonical correlation analysis. Through an experiment using a wooden bridge conducted by the Kullaa group in Finland, a comparison was performed among the cointegration method, the method combining canonical correlation analysis with cointegration, and the proposed method. It is shown that the first two methods are prone to influences by the number of monitored variables, and different numbers of monitored variables cause different identification results; however, the proposed method is insensitive to the number of monitored variables. Moreover, the proposed method results in a better false negative rate of damage identification than other methods. |
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| Keywords: | bridge engineering damage identification kernel canonical correlation analysis nonlinear correlation cointegration environmental influences |
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