基于主分量和独立分量分析的结构信号处理和损伤识别研究
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摘要
结构健康监测是一门综合性技术,涉及到多个学科,主要包括结构信号处理与损伤识别两大部分。目前对结构健康监测技术的研究都是围绕这两个部分开展的,是当前国内外研究的难点和热点之一。结构的状态是通过传感器信号来监测和评估的,由于传感器信号中有干扰因素的存在,为了提高数据的可靠性和精确性,并且更好的进行结构损伤状态识别和定位,需要有效、可靠的信号分析与处理方法。结构损伤识别问题,其关键是找到一个与结构损伤密切相关的特征指标。特征指标对结构系统参数的变化要有足够的敏感性,才能够根据该指标来分类识别结构损伤,完成损伤的确认、定位和定量。
主分量(PCA)反映了结构特征间的二阶统计特性,可以使得结构信号从高维空间转换到维数较低的特征空间。独立分量(ICA)反映了结构特征间的高阶统计特性,比PCA更进一层,它不只要求各分量间去相关,而且还要求各分量相互统计独立。不管PCA还是ICA,在统计意义上都反映了结构状态间的本质特性。
本文将主分量和独立分量分析方法引入到土木工程结构的信号处理和损伤识别方法中,利用它们的统计特性对结构信号进行降噪处理和损伤特征提取。本文的主要研究工作可以分为两部分:
(一)基于PCA和ICA的结构信号处理研究
1.基于PCA的理论,利用它的二阶统计特性来消除结构信号之间的相关性,选取低维主分量特征来表征传感器信号的特性,从而实现结构信号的降维。通过对振动实验信号进行降维处理,试验结果表明选取的少数主分量特征包含了结构信号的主要特征。
2.提出了分辨噪声和结构振动有用信号的方法。分析了噪声的来源及其在频域内的特点,介绍了抗噪声干扰的技术。由于噪声的频谱以及统计特性与振动信号不同,以此来区分辨别。通过数值算例和振动实验信号分析说明了噪声与结构振动信号的这些特性。
3.提出了基于ICA的结构振动信号降噪处理算法。该算法利用噪声与结构振动信号相互独立的特点,从传感器信号中部分或全部分离出噪声。同时,提出通过对同测点增加扩展通道和多通道信号增设噪声通道的方法进行降噪处理,该降噪方法不仅对单通道适用,而且可以对多通道传感器信号进行降噪处理,只需增加噪声通道来扩展传感器信号。通过实验验证了这两种方法的可行性和有效性。
(二)基于PCA和ICA的结构损伤特征提取研究
1.引入相关系数来度量结构两种状态的统计特征之间的相关度,由此分别构造了基于PCA和ICA的损伤特征提取指标。PCA和ICA特征提取指标可以反映结构状态的本质统计特征。
2.基于PCA理论分析了对结构振动信号的统计特性,提出了PCA损伤特征提取方法。为了减少数据的计算量和突出指标的损伤特性,在指标的构造过程中进行降维,并且讨论了如何有效地选取恰当的主分量个数来表征结构的状态。最后通过固支梁振动实验数据验证了PCA特征指标识别结构损伤的可行性。
3.讨论了ICA基滤波对不同状态的结构振动信号的统计量化特性,提出了基于ICA特征指标的结构特征提取方法,通过固支梁振动实验分析了确定不同的基准状态对结构损伤的影响。
4.提出了结构分区损伤检测方法,解决了ICA特征指标无法识别损伤位置的问题;通过对区段ICA特征指标的比较,可以识别出结构的损伤位置。
The structure health monitoring is a comprehensive technology and has become one of the most active reseach areas. Structure signal processing and damage identification are the mainly two major parts of health monitori system.The structure condition is monitored and assessed by sensor signals, namely the characteristic indexes are extracted from the sensor signals to monitor and diagnose structure condition. Because many disturbance factors exist in the sensor signals, the effective and reliable signal analysis processing method is proposed to enhance the reliability and accuracy of data, so as to better indentify the structure damage condition and localization. The key problem of structure damage identification is to find out the characteristic indexes which are enough sensitive to the change of structure system parameter. Therefore, signal processing and damage identification on structure sensor signals has the academic value and practical significance.
The principal components analysis (PCA) reflects the second-order statistical characteristic of structure property and can transform the structure signals from the high dimension space to the low dimension characteristic space. The independent component analysis (ICA) reflects the higher order statistical characteristic of structure property. Correspondingly to PCA, ICA gets rid of the correlation of the components; moreover require the components statistical independent. No matter PCA or ICA, they all reflect the essential characteristic between structure conditions in statistical significance.
The method of PCA and ICA are introduced into signal processing and damage identification of civil engineering structure. The main research work of this article is followed:
1. Study of structural signal processing based on PCA and ICA
(1) Based on the PCA theory, the relativity between structure signals is eliminated by their second-order statistical characteristic. The low dimension characteristic of PCA represent the property of sensor signals, thus the dimensionality of structure signals is reduced. The dimensionality reduction processing of vibration experimental signals indicates that the minority components have contained the main characteristic of structure signals.
(2) The noise origin and its characteristic in frequency domain is analyzed, the anti-noise technology is presented. The frequency spectrum and the statistical property of noise are different from the vibration signal so as to differentiate them. These characteristics are illustrated through the numerical example and the vibration experiment signal analysis.
(3) The noise reduction algorithm based on ICA is proposed to structure vibration signal processing. Because of the independence characteristic of the noise and structural vibration signals, the noise can be partly or completely separated from the sensor signals with ICA algorithm. At the same time, the article proposes two methods of sensor collocation. Noise is reduced with increasing the expansion channel of the same sensor point and the addition noise channel. The data processing of vibration experiment validates the feasibility and validity of the two methods.
2. Study of structure signal processing based on PCA and ICA
(1) Introduces the correlation coefficient to measure the comparability between the two structure conditions, and the damage characteristic extraction indexes based on PCA and ICA are constructed. The two extraction indexes can reflect the statistical characteristic of structure condition.
(2) In order to reduce the computation quantity of the data and extract the damage characteristic, PCA damage characteristic indexes is constructed to reduce data dimensionality. The number of principal component is confirmed by the accumulative contribution ratio of PCA. The feasibility of PCA characteristic index is validated through the structure vibration experiment data.
(3) The statistical characteristic of ICA benchmark filter between different condition structure vibration signals is discussed in the article. The damage characteristic index basis of ICA is constructed to identify the structure damage. The influence of different benchmark condition to damage identification has analyzed through the vibration experiment.
(4) The method of structure district damage examination is proposed to recognize the damage state and position.
主分量(PCA)反映了结构特征间的二阶统计特性,可以使得结构信号从高维空间转换到维数较低的特征空间。独立分量(ICA)反映了结构特征间的高阶统计特性,比PCA更进一层,它不只要求各分量间去相关,而且还要求各分量相互统计独立。不管PCA还是ICA,在统计意义上都反映了结构状态间的本质特性。
本文将主分量和独立分量分析方法引入到土木工程结构的信号处理和损伤识别方法中,利用它们的统计特性对结构信号进行降噪处理和损伤特征提取。本文的主要研究工作可以分为两部分:
(一)基于PCA和ICA的结构信号处理研究
1.基于PCA的理论,利用它的二阶统计特性来消除结构信号之间的相关性,选取低维主分量特征来表征传感器信号的特性,从而实现结构信号的降维。通过对振动实验信号进行降维处理,试验结果表明选取的少数主分量特征包含了结构信号的主要特征。
2.提出了分辨噪声和结构振动有用信号的方法。分析了噪声的来源及其在频域内的特点,介绍了抗噪声干扰的技术。由于噪声的频谱以及统计特性与振动信号不同,以此来区分辨别。通过数值算例和振动实验信号分析说明了噪声与结构振动信号的这些特性。
3.提出了基于ICA的结构振动信号降噪处理算法。该算法利用噪声与结构振动信号相互独立的特点,从传感器信号中部分或全部分离出噪声。同时,提出通过对同测点增加扩展通道和多通道信号增设噪声通道的方法进行降噪处理,该降噪方法不仅对单通道适用,而且可以对多通道传感器信号进行降噪处理,只需增加噪声通道来扩展传感器信号。通过实验验证了这两种方法的可行性和有效性。
(二)基于PCA和ICA的结构损伤特征提取研究
1.引入相关系数来度量结构两种状态的统计特征之间的相关度,由此分别构造了基于PCA和ICA的损伤特征提取指标。PCA和ICA特征提取指标可以反映结构状态的本质统计特征。
2.基于PCA理论分析了对结构振动信号的统计特性,提出了PCA损伤特征提取方法。为了减少数据的计算量和突出指标的损伤特性,在指标的构造过程中进行降维,并且讨论了如何有效地选取恰当的主分量个数来表征结构的状态。最后通过固支梁振动实验数据验证了PCA特征指标识别结构损伤的可行性。
3.讨论了ICA基滤波对不同状态的结构振动信号的统计量化特性,提出了基于ICA特征指标的结构特征提取方法,通过固支梁振动实验分析了确定不同的基准状态对结构损伤的影响。
4.提出了结构分区损伤检测方法,解决了ICA特征指标无法识别损伤位置的问题;通过对区段ICA特征指标的比较,可以识别出结构的损伤位置。
The structure health monitoring is a comprehensive technology and has become one of the most active reseach areas. Structure signal processing and damage identification are the mainly two major parts of health monitori system.The structure condition is monitored and assessed by sensor signals, namely the characteristic indexes are extracted from the sensor signals to monitor and diagnose structure condition. Because many disturbance factors exist in the sensor signals, the effective and reliable signal analysis processing method is proposed to enhance the reliability and accuracy of data, so as to better indentify the structure damage condition and localization. The key problem of structure damage identification is to find out the characteristic indexes which are enough sensitive to the change of structure system parameter. Therefore, signal processing and damage identification on structure sensor signals has the academic value and practical significance.
The principal components analysis (PCA) reflects the second-order statistical characteristic of structure property and can transform the structure signals from the high dimension space to the low dimension characteristic space. The independent component analysis (ICA) reflects the higher order statistical characteristic of structure property. Correspondingly to PCA, ICA gets rid of the correlation of the components; moreover require the components statistical independent. No matter PCA or ICA, they all reflect the essential characteristic between structure conditions in statistical significance.
The method of PCA and ICA are introduced into signal processing and damage identification of civil engineering structure. The main research work of this article is followed:
1. Study of structural signal processing based on PCA and ICA
(1) Based on the PCA theory, the relativity between structure signals is eliminated by their second-order statistical characteristic. The low dimension characteristic of PCA represent the property of sensor signals, thus the dimensionality of structure signals is reduced. The dimensionality reduction processing of vibration experimental signals indicates that the minority components have contained the main characteristic of structure signals.
(2) The noise origin and its characteristic in frequency domain is analyzed, the anti-noise technology is presented. The frequency spectrum and the statistical property of noise are different from the vibration signal so as to differentiate them. These characteristics are illustrated through the numerical example and the vibration experiment signal analysis.
(3) The noise reduction algorithm based on ICA is proposed to structure vibration signal processing. Because of the independence characteristic of the noise and structural vibration signals, the noise can be partly or completely separated from the sensor signals with ICA algorithm. At the same time, the article proposes two methods of sensor collocation. Noise is reduced with increasing the expansion channel of the same sensor point and the addition noise channel. The data processing of vibration experiment validates the feasibility and validity of the two methods.
2. Study of structure signal processing based on PCA and ICA
(1) Introduces the correlation coefficient to measure the comparability between the two structure conditions, and the damage characteristic extraction indexes based on PCA and ICA are constructed. The two extraction indexes can reflect the statistical characteristic of structure condition.
(2) In order to reduce the computation quantity of the data and extract the damage characteristic, PCA damage characteristic indexes is constructed to reduce data dimensionality. The number of principal component is confirmed by the accumulative contribution ratio of PCA. The feasibility of PCA characteristic index is validated through the structure vibration experiment data.
(3) The statistical characteristic of ICA benchmark filter between different condition structure vibration signals is discussed in the article. The damage characteristic index basis of ICA is constructed to identify the structure damage. The influence of different benchmark condition to damage identification has analyzed through the vibration experiment.
(4) The method of structure district damage examination is proposed to recognize the damage state and position.
引文
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