Morlet小波变换理论与应用研究及软件实现
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摘要
小波分析作为时频分析方法中一种新的信号处理技术,近年来取得了飞速的发展并在各种实际工程领域中获得了广泛的应用。本文以非正交的Morlet小波作为母小波,深入研究了其时频域分析的特性以及在模态参数识别中的应用,并在理论算法研究的基础上开发了N-DTAS软件。全文主要包括以下内容:
(1)研究了Morlet小波变换的时频域分析的特性。分析了小波变换中伸缩因子a和平移因子b的改变对其时域和频域分辨率的影响关系;从Parseval定理和卷积定理的角度推导了非正交小波变换系数的快速、简单、实用的算法;
(2)针对具有输入输出数据的模态参数识别,研究了基于自由响应数据的Morlet小波识别技术。由小波变换系数模的幅值和相位拟合计算出系统的模态频率和阻尼比;对于振型的识别提出了基于最小二乘法的识别技术;从识别密集模态的角度研究了基于改进的Morlet小波的模态参数识别技术,并推导了小波中心频率f 0和小波因子N的关系;三自由度仿真算例和GARTEUR飞机模型的识别验证了基于改进Morlet小波对密集模态的识别是十分有效的;
(3)研究了将非正交的Morlet小波用于仅有输出数据的模态参数识别技术。提出了将相关函数而非随机减量函数作为系统的时间响应函数,采用Morlet小波进行模态参数识别的方法;相比传统的将随机减量函数作为系统的时间响应函数,该法具有明显的优点:采用频域中相关函数的无偏估计算法,计算速度快,程序运行效率高,同时由于在频域中采用了分段平均的方法,有效提升了相关函数矩阵(即自由响应数据矩阵)的信噪比,提高了模态参数(特别是阻尼比)的识别精度;二层楼的仿真算例及潮白河桥实测响应数据的识别结果验证了该法的可行性;
(4)在LabVIEW平台下开发了数据采集与信号分析软件——N-DTAS,该软件不仅具有传统基于FFT的分析功能,同时也开发了Morlet小波的模态参数识别功能。从程序代码的编写到安装软件的制作,研究了LabVIEW平台下的开发设计技术,主要包括:GPIB接口的仪器驱动技术、多线程技术、DLL调用技术、Queue技术、界面设计技术、文件管理技术以及软件的安装制作技术等。从软件的使用角度通过实验全面验证了N-DTAS各个功能模块的有效性及实用性。
In recent years, wavelet analysis as a new kind of time-frequency representation technique, has obtained rapid development and widespread application in different engineering field. Based on non-orthogonal Morlet wavelet, its analysis characteristic in time-frequency domain and application in modal parameter identification are studied deeply and systemically in this dissertation. In addition, on the foundation of theory and algorithm research, N-DTAS software has been developed based on LabVIEW platform. The main content is as follows:
The relation between the change of dilatation factor a and translation factor b and the resolution of time and frequency domain is investigated in detail. Fast, simple and practical computational approach of non-orthogonal wavelet coefficient is presented from both convolution and Parseval theorem point of view.
For the identification of modal parameters with input and output data, the method using the free response of analysed system based on tradional and modified Morlet wavelet is researched. Modal frequency and damping ratio can be obtained by fitting the wavelet transform coefficient’s modulu and phase. Especially the idendification of mode shape based on least square and the condition satisfyied between wavelet center frequency f0 and wavelet factor N are proposed. The result of three degree of freedom simulation system and GARTEUR aircraft model shows that the modified Morlet wavelet is very suitable for modal parameters identification with closed mode frequency.
The method substituting not random decrement function but correlation function for time response function is presented for the identification of modal parameters with only output data. In contrast to the traditional method extracting system free response via RDT, the obvious advantage is that, the unbiased cross-correlation estimation based on FFT has faster computing speed and average technique in frequency domain can enhance SNR level, and the identification result especially damping ratio has the higher precision. The efficency of the method has been demonstrated by two-storey building and Chao-bai bridge example results.
N-DTAS software for data acquisition and signal processing, which has the function based on not only traditional FFT but also wavelet analysis for modal parameter identification, is developed based on LabVIEW platform. In this dissertation, the key LabVIEW advanced programming technique such as GPIB driver, Multithread, DLL, Queue, GUI, VI Sever, file management and software installer are described in detail.
(1)研究了Morlet小波变换的时频域分析的特性。分析了小波变换中伸缩因子a和平移因子b的改变对其时域和频域分辨率的影响关系;从Parseval定理和卷积定理的角度推导了非正交小波变换系数的快速、简单、实用的算法;
(2)针对具有输入输出数据的模态参数识别,研究了基于自由响应数据的Morlet小波识别技术。由小波变换系数模的幅值和相位拟合计算出系统的模态频率和阻尼比;对于振型的识别提出了基于最小二乘法的识别技术;从识别密集模态的角度研究了基于改进的Morlet小波的模态参数识别技术,并推导了小波中心频率f 0和小波因子N的关系;三自由度仿真算例和GARTEUR飞机模型的识别验证了基于改进Morlet小波对密集模态的识别是十分有效的;
(3)研究了将非正交的Morlet小波用于仅有输出数据的模态参数识别技术。提出了将相关函数而非随机减量函数作为系统的时间响应函数,采用Morlet小波进行模态参数识别的方法;相比传统的将随机减量函数作为系统的时间响应函数,该法具有明显的优点:采用频域中相关函数的无偏估计算法,计算速度快,程序运行效率高,同时由于在频域中采用了分段平均的方法,有效提升了相关函数矩阵(即自由响应数据矩阵)的信噪比,提高了模态参数(特别是阻尼比)的识别精度;二层楼的仿真算例及潮白河桥实测响应数据的识别结果验证了该法的可行性;
(4)在LabVIEW平台下开发了数据采集与信号分析软件——N-DTAS,该软件不仅具有传统基于FFT的分析功能,同时也开发了Morlet小波的模态参数识别功能。从程序代码的编写到安装软件的制作,研究了LabVIEW平台下的开发设计技术,主要包括:GPIB接口的仪器驱动技术、多线程技术、DLL调用技术、Queue技术、界面设计技术、文件管理技术以及软件的安装制作技术等。从软件的使用角度通过实验全面验证了N-DTAS各个功能模块的有效性及实用性。
In recent years, wavelet analysis as a new kind of time-frequency representation technique, has obtained rapid development and widespread application in different engineering field. Based on non-orthogonal Morlet wavelet, its analysis characteristic in time-frequency domain and application in modal parameter identification are studied deeply and systemically in this dissertation. In addition, on the foundation of theory and algorithm research, N-DTAS software has been developed based on LabVIEW platform. The main content is as follows:
The relation between the change of dilatation factor a and translation factor b and the resolution of time and frequency domain is investigated in detail. Fast, simple and practical computational approach of non-orthogonal wavelet coefficient is presented from both convolution and Parseval theorem point of view.
For the identification of modal parameters with input and output data, the method using the free response of analysed system based on tradional and modified Morlet wavelet is researched. Modal frequency and damping ratio can be obtained by fitting the wavelet transform coefficient’s modulu and phase. Especially the idendification of mode shape based on least square and the condition satisfyied between wavelet center frequency f0 and wavelet factor N are proposed. The result of three degree of freedom simulation system and GARTEUR aircraft model shows that the modified Morlet wavelet is very suitable for modal parameters identification with closed mode frequency.
The method substituting not random decrement function but correlation function for time response function is presented for the identification of modal parameters with only output data. In contrast to the traditional method extracting system free response via RDT, the obvious advantage is that, the unbiased cross-correlation estimation based on FFT has faster computing speed and average technique in frequency domain can enhance SNR level, and the identification result especially damping ratio has the higher precision. The efficency of the method has been demonstrated by two-storey building and Chao-bai bridge example results.
N-DTAS software for data acquisition and signal processing, which has the function based on not only traditional FFT but also wavelet analysis for modal parameter identification, is developed based on LabVIEW platform. In this dissertation, the key LabVIEW advanced programming technique such as GPIB driver, Multithread, DLL, Queue, GUI, VI Sever, file management and software installer are described in detail.
引文
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