小波脊线提取方法研究及其应用
发布时间：2019-03-30 16:16
【摘要】：小波脊线的提取是非平稳信号时频分析领域的一项重要内容。利用小波脊线包含的信息可以实现对信号瞬态特征的估计、对信号的分解重构和滤波，以及对系统的模态参数识别。目前，基于小波系数模极大值和相位信息的脊线提取算法有其各自的缺陷性。因此，为了减少小波变换的冗余性、提高脊线提取的效率、实现对多脊线信号的精确提取，本文研究了基于小波变换偏微分方程的脊线提取算法，探讨了算法中每个过程的实现以及各参数对结果的影响，并成功地将该算法应用于信号的分解重构以及系统的模态参数识别中，仿真实验的结果验证了算法的有效性和准确性。 本文的主要研究工作如下： （1）研究了连续小波变换的原理和实现过程，从信号小波脊线和小波骨架的概念、方法和应用等方面进行了理论研究，，对小波变换的基函数进行了变参数的改进。 （2）实现了一种基于小波变换偏微分方程的脊线提取算法。从小波脊线的模极大值定义和连续小波变换的偏微分方程开始，详细推导了算法的原理，设计了算法的数值计算实现步骤，结合该算法和改进的Morlet小波形式，对算法过程中多个参数的选取进行了详细地研究，并给出了各参数选取的基本原则。成功实现了该算法对信号小波脊线的提取和信号各分量的重构。 （3）将脊线提取算法应用于系统的模态参数识别中。研究了小波脊线和系统模态参数的关系，推导出了小波脊线识别模态参数的计算公式。分别用三自由度仿真系统和弧形结构模态实验对算法的有效性进行验证。仿真信号的识别结果具有很高的精度，弧形结构的模态频率识别具有较高的精度，分析了阻尼比产生偏差的原因。 （4）编制开发了基于MATLAB图形用户界面的小波时频-脊线分析软件。对软件进行了总体设计和需求分析，设计了软件的主界面，合理安排软件各功能模块的布局，对各功能模块进行了详细设计。选择简单实用的控件，采用结构化的编程方式，实现了算法的各个功能。对软件的主要功能模块进行了仿真测试与应用，验证了软件的算法有效性和技术实用性。
[Abstract]:Wavelet ridge extraction is an important content in time-frequency analysis of non-stationary signals. The information contained in the wavelet ridge line can be used to estimate the transient characteristics of the signal, to decompose and filter the signal, and to identify the modal parameters of the system. At present, ridge extraction algorithms based on wavelet coefficient modulus Maxima and phase information have their own defects. Therefore, in order to reduce the redundancy of wavelet transform, improve the efficiency of ridge line extraction, and realize the accurate extraction of multi-ridge line signal, the algorithm of ridge line extraction based on partial differential equation of wavelet transform is studied in this paper. The realization of each process in the algorithm and the influence of each parameter on the results are discussed. The algorithm is successfully applied to signal decomposition and reconstruction and modal parameter identification of the system. The simulation results show that the algorithm is effective and accurate. The main work of this paper is as follows: (1) the principle and realization process of continuous wavelet transform are studied, and the concept, method and application of signal wavelet ridge and wavelet skeleton are studied theoretically. The basis function of wavelet transform is improved by changing parameters. (2) A ridge line extraction algorithm based on partial differential equation of wavelet transform is implemented. Starting from the definition of modulus Maxima of wavelet ridge line and partial differential equation of continuous wavelet transform, the principle of the algorithm is deduced in detail, and the steps of numerical calculation are designed. The algorithm is combined with the improved Morlet wavelet form. The selection of several parameters in the process of the algorithm is studied in detail, and the basic principles of the selection of each parameter are given. The algorithm is successfully implemented to extract the wavelet ridge and reconstruct the components of the signal. (3) the ridge line extraction algorithm is applied to the modal parameter identification of the system. The relationship between the wavelet ridge line and the modal parameters of the system is studied, and the formula for calculating the modal parameters of the wavelet ridge line identification is derived. The validity of the algorithm is verified by the three-degree-of-freedom simulation system and the modal experiment of arc structure. The identification results of simulated signals have high accuracy, and the modal frequency identification of arc structures has high accuracy. The reasons for the deviation of damping ratio are analyzed. (4) the wavelet time-frequency-ridge analysis software based on MATLAB graphical user interface is developed. The main interface of the software is designed, the layout of each function module of the software is reasonably arranged, and the function modules are designed in detail. Select the simple and practical control, adopt the structured programming mode, realize each function of the algorithm. The main function modules of the software are simulated and tested and applied to verify the algorithm effectiveness and technical practicability of the software.
【学位授予单位】：南京航空航天大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.6
本文编号：2450253
[Abstract]:Wavelet ridge extraction is an important content in time-frequency analysis of non-stationary signals. The information contained in the wavelet ridge line can be used to estimate the transient characteristics of the signal, to decompose and filter the signal, and to identify the modal parameters of the system. At present, ridge extraction algorithms based on wavelet coefficient modulus Maxima and phase information have their own defects. Therefore, in order to reduce the redundancy of wavelet transform, improve the efficiency of ridge line extraction, and realize the accurate extraction of multi-ridge line signal, the algorithm of ridge line extraction based on partial differential equation of wavelet transform is studied in this paper. The realization of each process in the algorithm and the influence of each parameter on the results are discussed. The algorithm is successfully applied to signal decomposition and reconstruction and modal parameter identification of the system. The simulation results show that the algorithm is effective and accurate. The main work of this paper is as follows: (1) the principle and realization process of continuous wavelet transform are studied, and the concept, method and application of signal wavelet ridge and wavelet skeleton are studied theoretically. The basis function of wavelet transform is improved by changing parameters. (2) A ridge line extraction algorithm based on partial differential equation of wavelet transform is implemented. Starting from the definition of modulus Maxima of wavelet ridge line and partial differential equation of continuous wavelet transform, the principle of the algorithm is deduced in detail, and the steps of numerical calculation are designed. The algorithm is combined with the improved Morlet wavelet form. The selection of several parameters in the process of the algorithm is studied in detail, and the basic principles of the selection of each parameter are given. The algorithm is successfully implemented to extract the wavelet ridge and reconstruct the components of the signal. (3) the ridge line extraction algorithm is applied to the modal parameter identification of the system. The relationship between the wavelet ridge line and the modal parameters of the system is studied, and the formula for calculating the modal parameters of the wavelet ridge line identification is derived. The validity of the algorithm is verified by the three-degree-of-freedom simulation system and the modal experiment of arc structure. The identification results of simulated signals have high accuracy, and the modal frequency identification of arc structures has high accuracy. The reasons for the deviation of damping ratio are analyzed. (4) the wavelet time-frequency-ridge analysis software based on MATLAB graphical user interface is developed. The main interface of the software is designed, the layout of each function module of the software is reasonably arranged, and the function modules are designed in detail. Select the simple and practical control, adopt the structured programming mode, realize each function of the algorithm. The main function modules of the software are simulated and tested and applied to verify the algorithm effectiveness and technical practicability of the software.
【学位授予单位】：南京航空航天大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.6
【参考文献】
相关期刊论文 前5条
1 柳小勤;岳林;朱如鹏;;连续小波变换应用于密集模态参数识别[J];南京航空航天大学学报;2007年04期
2 岳林,费庆国,张令弥;基于Morlet小波滤波提高系统参数识别精度的方法(英文)[J];Transactions of Nanjing University of Aeronautics & Astronau;2005年03期
3 王兵,羿旭明;一种提取小波脊线的迭代算法[J];数学杂志;2005年03期
4 黎海妹;陈建文;;一种改进的小波脊提取算法[J];通信技术;2010年04期
5 郁春来,万建伟,徐如海,韩彦明;改进小波脊线法算法分析和仿真[J];现代雷达;2005年08期
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