基于独立分量分析的结构模态分析与损伤诊断
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摘要
土木工程结构是国家基础设施的重要组成部分,直接关系到人民的生活和安全。近年来,越来越多的结构健康监测系统安装到桥梁、大跨空间结构等大型土木工程结构中,但决定健康监测系统成败的系统识别和损伤识别技术仍未从根本上解决。因此,进一步研究适应大型土木工程结构实时监测所需的模态分析和损伤识别方法具有重要价值。本文将新的信号分析技术(独立分量分析、希尔伯特-黄变换)引入到结构的系统识别和损伤识别中,为发展满足大型土木结构健康监测所需的工作模态参数识别和损伤识别技术提供有效手段。本文的主要研究工作如下：
(1)在简要介绍健康监测核心技术的基础上,阐述了本课题的研究目的与意义,系统地回顾和综述了现有结构模态参数识别和损伤识别方法的应用背景、理论意义与研究现状。
(2)对独立分量分析的基本原理、衡量随机变量独立性的判据准则,以及在独立分量分析中经常采用的预处理方法进行了介绍与讨论。重点讨论了基于负熵的固定点算法,即FastICA算法。独立分量分析以统计独立性和非高斯性为原则,是从多元(多维)数据中寻找其内在因子或成分的一种有效方法。采用的FastICA算法能有效地对信号中的源成分进行提取,并具有良好的稳定性。
(3)探讨了多自由度系统动力响应的模态坐标与独立分量之间的关系。多自由度系统在自由振动和宽带随机激励下的响应,其模态坐标满足独立分量分析关于源信号的相关假定,可以看作是一种特殊的独立源信号。分别通过一个三自由度体系和一个简支梁的数值仿真算例对以上结论进行验证,结果表明,应用独立分量分析方法可以从多自由度系统的自振响应或随机响应中提取出各阶模态坐标,同时估计出模态振型向量。
(4)提出了基于独立分量分析的结构工作模态参数识别方法。利用独立分量分析方法直接从结构振动响应时域信号中提取出与结构模态坐标相对应的独立分量并估计出模态振型,再对单一成分的独立分量进行Hilbert变换计算结构的固有频率和阻尼比(若独立分量为随机响应需先利用随机减量法提取自振响应)。结合数值仿真算例与振动实验模态分析,验证了该方法用于结构工作模态参数识别的有效性。
(5)通过理论分析、数值仿真对基于曲率模态差分原理的结构损伤识别方法进行了讨论。研究结果表明：曲率类指标比位移类指标对损伤敏感；曲率模态对模态节点损伤不敏感,对于非模态节点损伤,曲率模态可以实现对损伤进行定位,并且曲率模态突变差与损伤量近似呈线性关系；曲率模态变化率是比曲率模态更为敏感的损伤指标,无论模态节点损伤或非模态节点损伤均在损伤处发生突变,适合于结构损伤识别与定位。
(6)提出基于Hilbert-Huang变换的结构损伤特征提取方法。研究表明,无论位移模态信号或曲率模态信号对于小损伤均不能明显表现出来,通过EEMD自适应的多尺度分解能力来对模态信号中的微弱损伤信息进行特征提取,再结合Hilbert谱的时频分析,可有效地对损伤进行识别与定位。
Civil engineering structures are important part of national infrastructures that are directly related to people's daily life. In recent years, more and more structural health monitoring (SHM) system has been installed in the civil engineering structures such as bridges, long-span space structures, etc. However, as one of the key techniques, the system identification and damage detection has never been ultimately resolved. Therefore, the further research of modal analysis and damage detection method adapting to on-line SHM system of large civil engineering structures has important theoretical significance and practical value. In this dissertation, some new signal analysis techniques such as independent component analysis (ICA), Hilbert-Huang Transform (HHT) have been used for the system identification and damage detection of structures. Some effective means have been proposed, which meeting the need of SHM. The main contents are listed as follow:
(1) Based on the introduction of the research state of SHM system, the purpose and significance of this thesis have been explained. The theory significance, the application background, the present development and research results have obtained of structural modal parameter identification and damage detection methods have been commented in detail.
(2) The basic principle of ICA, criterion of the independence of random variables have been presented and discussed, as well as the pretreatment methods often used in ICA. More focus has been on the fixed-point algorithm based on negentropy for ICA, which is also called FastICA. ICA is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. FastICA algorithm is valid for extracting source component, and works well and stably.
(3) The relation between modal coordinates of MDOF system and independent components has been discussed. For free and random vibrations of MDOF systems, modal coordinates have been considered as a specific case of sources that satisfy the relevant assumptions about the source of ICA. To support the previous theoretical findings, numerical experiments of a discrete system of three masses and a free beam have been carried out respectively. The results indicate that ICA is robust to extracting the modal coordinates from dynamic response of MDOF system under free and random vibrations, as well as mode shape vectors.
(4) The output-only modal parameter identification method based on ICA has been proposed. Firstly, the modal coordinates and mode shape vectors have been obtained from dynamic response of structure directly by using ICA. Then, the natural frequency and damping ratio of structure have been calculated from modal coordinates by Hilbert transform. For random vibration of structure, the free responses shoud be extracted from independent components by random decrement technique (RDT) before Hilbert transform. Numerical simulation and experimental results indicate that the proposed method is robust to mode shape extraction and suitable for output-only structural modal parameter identification.
(5) The structural damage detection method based on curvature mode difference theory has been discussed through theoretical analysis and numerical simulation. The results show that:curvature based damage features are superior to that based displacement; curvature mode is not sensitive to damage located in the mode node; the change rate of curvature mode is more sensitive to damage than curvature mode, whether damage located in mode node or not can be detected.
(6) A structural damage detection method based on Hilbert-Huang Transform has been proposed for micro-damage of structure. The ensemble empirical mode decomposition (EEMD) method is used to decompose the modal signal adaptively, the changes of the characteristic frequency are obtained using Hilbert spectrum, and the location of damage are identified effectively.
(1)在简要介绍健康监测核心技术的基础上,阐述了本课题的研究目的与意义,系统地回顾和综述了现有结构模态参数识别和损伤识别方法的应用背景、理论意义与研究现状。
(2)对独立分量分析的基本原理、衡量随机变量独立性的判据准则,以及在独立分量分析中经常采用的预处理方法进行了介绍与讨论。重点讨论了基于负熵的固定点算法,即FastICA算法。独立分量分析以统计独立性和非高斯性为原则,是从多元(多维)数据中寻找其内在因子或成分的一种有效方法。采用的FastICA算法能有效地对信号中的源成分进行提取,并具有良好的稳定性。
(3)探讨了多自由度系统动力响应的模态坐标与独立分量之间的关系。多自由度系统在自由振动和宽带随机激励下的响应,其模态坐标满足独立分量分析关于源信号的相关假定,可以看作是一种特殊的独立源信号。分别通过一个三自由度体系和一个简支梁的数值仿真算例对以上结论进行验证,结果表明,应用独立分量分析方法可以从多自由度系统的自振响应或随机响应中提取出各阶模态坐标,同时估计出模态振型向量。
(4)提出了基于独立分量分析的结构工作模态参数识别方法。利用独立分量分析方法直接从结构振动响应时域信号中提取出与结构模态坐标相对应的独立分量并估计出模态振型,再对单一成分的独立分量进行Hilbert变换计算结构的固有频率和阻尼比(若独立分量为随机响应需先利用随机减量法提取自振响应)。结合数值仿真算例与振动实验模态分析,验证了该方法用于结构工作模态参数识别的有效性。
(5)通过理论分析、数值仿真对基于曲率模态差分原理的结构损伤识别方法进行了讨论。研究结果表明：曲率类指标比位移类指标对损伤敏感；曲率模态对模态节点损伤不敏感,对于非模态节点损伤,曲率模态可以实现对损伤进行定位,并且曲率模态突变差与损伤量近似呈线性关系；曲率模态变化率是比曲率模态更为敏感的损伤指标,无论模态节点损伤或非模态节点损伤均在损伤处发生突变,适合于结构损伤识别与定位。
(6)提出基于Hilbert-Huang变换的结构损伤特征提取方法。研究表明,无论位移模态信号或曲率模态信号对于小损伤均不能明显表现出来,通过EEMD自适应的多尺度分解能力来对模态信号中的微弱损伤信息进行特征提取,再结合Hilbert谱的时频分析,可有效地对损伤进行识别与定位。
Civil engineering structures are important part of national infrastructures that are directly related to people's daily life. In recent years, more and more structural health monitoring (SHM) system has been installed in the civil engineering structures such as bridges, long-span space structures, etc. However, as one of the key techniques, the system identification and damage detection has never been ultimately resolved. Therefore, the further research of modal analysis and damage detection method adapting to on-line SHM system of large civil engineering structures has important theoretical significance and practical value. In this dissertation, some new signal analysis techniques such as independent component analysis (ICA), Hilbert-Huang Transform (HHT) have been used for the system identification and damage detection of structures. Some effective means have been proposed, which meeting the need of SHM. The main contents are listed as follow:
(1) Based on the introduction of the research state of SHM system, the purpose and significance of this thesis have been explained. The theory significance, the application background, the present development and research results have obtained of structural modal parameter identification and damage detection methods have been commented in detail.
(2) The basic principle of ICA, criterion of the independence of random variables have been presented and discussed, as well as the pretreatment methods often used in ICA. More focus has been on the fixed-point algorithm based on negentropy for ICA, which is also called FastICA. ICA is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. FastICA algorithm is valid for extracting source component, and works well and stably.
(3) The relation between modal coordinates of MDOF system and independent components has been discussed. For free and random vibrations of MDOF systems, modal coordinates have been considered as a specific case of sources that satisfy the relevant assumptions about the source of ICA. To support the previous theoretical findings, numerical experiments of a discrete system of three masses and a free beam have been carried out respectively. The results indicate that ICA is robust to extracting the modal coordinates from dynamic response of MDOF system under free and random vibrations, as well as mode shape vectors.
(4) The output-only modal parameter identification method based on ICA has been proposed. Firstly, the modal coordinates and mode shape vectors have been obtained from dynamic response of structure directly by using ICA. Then, the natural frequency and damping ratio of structure have been calculated from modal coordinates by Hilbert transform. For random vibration of structure, the free responses shoud be extracted from independent components by random decrement technique (RDT) before Hilbert transform. Numerical simulation and experimental results indicate that the proposed method is robust to mode shape extraction and suitable for output-only structural modal parameter identification.
(5) The structural damage detection method based on curvature mode difference theory has been discussed through theoretical analysis and numerical simulation. The results show that:curvature based damage features are superior to that based displacement; curvature mode is not sensitive to damage located in the mode node; the change rate of curvature mode is more sensitive to damage than curvature mode, whether damage located in mode node or not can be detected.
(6) A structural damage detection method based on Hilbert-Huang Transform has been proposed for micro-damage of structure. The ensemble empirical mode decomposition (EEMD) method is used to decompose the modal signal adaptively, the changes of the characteristic frequency are obtained using Hilbert spectrum, and the location of damage are identified effectively.
引文
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