系统模态参数辨识的连续小波方法研究
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摘要
对机械系统进行模态分析和参数识别是分析系统动力学性能,进行故障诊断等多种研究必不可少的手段之一。模态参数辨识的时频分析方法是继频域和时域方法之后新发展起来的一种模态分析方法。相较于频域和时域模态分析方法,连续小波模态分析方法利用小波分析在数学处理能力上的优势,辨识更为精确,对含噪信号不敏感,方法简单有效,对这一方法进行深入地研究,有重大的理论意义和现实意义.本文所涉及的主要工作及创造性成果如下:
本文对模态分析小波辨识方法的基础——脊线提取方法进行了详细的研究。在介绍了脊线提取的平稳相位理论的基础上,建立了连续小波变换脊线识别的基本方法。通过对利用小波变换的相位和模值信息提取脊线的识别算法进行比较研究,选择了更适于模态参数提取的Crazy Climbers算法,并以能量准则为基础改进了原有算法对噪声敏感这一缺点。仿真试验表明,改进Crazy Climber算法更适合于多自由度系统响应信号的小波脊线提取,对噪声具有很高的鲁棒性。
本文选择Morlet小波作为系统辨识研究的基本小波。并针对小波变换时频关系的特点改进了原有小波函数,用以平衡小波函数时间、频率两方面的性质。采用这一算进行了仿真研究。仿真结果表明,该方法模态参数提取准确,对噪声不敏感。通过对悬臂梁的实验研究表明,该方法较一般频域方法有更高的辨识精度,可准确的识别悬臂梁模态参数。
本文给出了不同尺度下边缘效应影响范围的划定方法。在介绍了常用改进方法的基础上,针对多自由度系统模态参数辨识的需要,给出了一种补偿函数法来解决这一问题。通过仿真实验表明,该方法计算负担小,可极大改善小波变换的边缘效应。
本文给出了基于连续小波变换的模态参数提取方法可辨识密集模态的基本条件。针对密集模态对参数辨识所带来的影响,本文给出了基于改进Morlet小波的改进算法,并以某三阶系统进行仿真实验。实验结果表明,该方法可极大改善由密集模态带来的频率混叠问题,参数辨识准确,可满足密集模态参数辨识的需要。
This paper deals with the use of the continuous wavelet transform (CWT) for system identification purposes. CWT method is a new way to the identification of modal parameter. This time-frequency-domain method is a new developed method after time–domain and frequency-domain method. It has been proved that CWT method was exact at the identification of modal parameter, and was not sensitive to the noise. The main work and harvests of this paper are as follows:
The wavelet ridge extraction method (REM) was studied in this paper. REM was used for the extraction of temporary frequency at before. REMs developed for this purpose would not work for modal parameter identification. A new method is introduced in this paper, called Crazy Climber method. Crazy Climber method can extract several ridges in the same time. It can be used for modal parameter identification of multi-degree-of-freedom (MDOF). But this method is sensitive to the noise. A improved study was introduced in this paper. The simulate result shows that the improved Crazy Climber method is not sensitive to the noise.
Morlet wavelet was selected in this paper for identification purpose. A optimize wavelet method was used for the best time and frequency performances. A cantilever was tested to validate this method. The test result shows that the method is suit to the modal parameter identification.
The edge-effect of wavelets was analyzed in this paper. A edge-effect measure method was introduced in this paper. In order to the MDOF identification, an equalizing function method was put forward. The simulate result shows that this method can modify the edge effected wavelet transform ridge commendably.
The mass model question was studied in this paper. An estimate rule was introduced in this paper. This rule could divide mass models from normal models. A improved Morlet wavelet is used for the mass model estimation. A simulated 3DOF system was tested by the wavelet. The result shows that the improved Morlet wavelet is useful for mass model identification.
本文对模态分析小波辨识方法的基础——脊线提取方法进行了详细的研究。在介绍了脊线提取的平稳相位理论的基础上,建立了连续小波变换脊线识别的基本方法。通过对利用小波变换的相位和模值信息提取脊线的识别算法进行比较研究,选择了更适于模态参数提取的Crazy Climbers算法,并以能量准则为基础改进了原有算法对噪声敏感这一缺点。仿真试验表明,改进Crazy Climber算法更适合于多自由度系统响应信号的小波脊线提取,对噪声具有很高的鲁棒性。
本文选择Morlet小波作为系统辨识研究的基本小波。并针对小波变换时频关系的特点改进了原有小波函数,用以平衡小波函数时间、频率两方面的性质。采用这一算进行了仿真研究。仿真结果表明,该方法模态参数提取准确,对噪声不敏感。通过对悬臂梁的实验研究表明,该方法较一般频域方法有更高的辨识精度,可准确的识别悬臂梁模态参数。
本文给出了不同尺度下边缘效应影响范围的划定方法。在介绍了常用改进方法的基础上,针对多自由度系统模态参数辨识的需要,给出了一种补偿函数法来解决这一问题。通过仿真实验表明,该方法计算负担小,可极大改善小波变换的边缘效应。
本文给出了基于连续小波变换的模态参数提取方法可辨识密集模态的基本条件。针对密集模态对参数辨识所带来的影响,本文给出了基于改进Morlet小波的改进算法,并以某三阶系统进行仿真实验。实验结果表明,该方法可极大改善由密集模态带来的频率混叠问题,参数辨识准确,可满足密集模态参数辨识的需要。
This paper deals with the use of the continuous wavelet transform (CWT) for system identification purposes. CWT method is a new way to the identification of modal parameter. This time-frequency-domain method is a new developed method after time–domain and frequency-domain method. It has been proved that CWT method was exact at the identification of modal parameter, and was not sensitive to the noise. The main work and harvests of this paper are as follows:
The wavelet ridge extraction method (REM) was studied in this paper. REM was used for the extraction of temporary frequency at before. REMs developed for this purpose would not work for modal parameter identification. A new method is introduced in this paper, called Crazy Climber method. Crazy Climber method can extract several ridges in the same time. It can be used for modal parameter identification of multi-degree-of-freedom (MDOF). But this method is sensitive to the noise. A improved study was introduced in this paper. The simulate result shows that the improved Crazy Climber method is not sensitive to the noise.
Morlet wavelet was selected in this paper for identification purpose. A optimize wavelet method was used for the best time and frequency performances. A cantilever was tested to validate this method. The test result shows that the method is suit to the modal parameter identification.
The edge-effect of wavelets was analyzed in this paper. A edge-effect measure method was introduced in this paper. In order to the MDOF identification, an equalizing function method was put forward. The simulate result shows that this method can modify the edge effected wavelet transform ridge commendably.
The mass model question was studied in this paper. An estimate rule was introduced in this paper. This rule could divide mass models from normal models. A improved Morlet wavelet is used for the mass model estimation. A simulated 3DOF system was tested by the wavelet. The result shows that the improved Morlet wavelet is useful for mass model identification.
引文
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