多尺度线调频基稀疏信号分解及其在齿轮箱故障诊断中的应用
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摘要
齿轮箱是机械设备中一种必不可少的连接和传递动力通用零部件,也是一种易于发生故障的零部件。研究齿轮箱的状态监测与故障诊断技术,对于保障机械设备的安全、稳定运行具有重要意义。
基于振动信号分析处理的齿轮箱状态监测与故障诊断方法由于具有可在线、实时、非损伤、诊断便捷准确等特点,己广泛应用于工程实际。齿轮箱发生故障时,故障产生的冲击形成不同程度和形态的振动信号调制现象,如何有效的提取具有故障特征的振动信号调制边频带是齿轮箱故障诊断技术的重要研究内容。针对转速变化的复杂齿轮箱动态调制边频带难以提取和现有时频分析方法时频聚集性不够、抗噪能力弱、不能有效分析瞬时频率大范围变化的非平稳信号问题,本文在国家自然科学基金项目“多尺度线调频基稀疏信号分解方法及其在机械故障诊断中的应用研究”(项目批准号:50875078)和高等学校博士学科点专项科研基金项目“基于多尺度线调频基的稀疏信号分解包络解调方法及其在齿轮箱故障诊断中的应用研究”(项目批准号:20090161110006)资助下,研究提出了一种新的信号处理方法—多尺度线调频基稀疏信号分解方法,并将其应用于转速变化的复杂齿轮箱故障诊断,深入系统地研究了基于多尺度线调频基稀疏信号分解方法的变转速齿轮箱动态调制边频带提取、阶比跟踪转速提取、多分量非平稳信号相位函数提取以及自适应时变滤波器设计等问题,主要研究工作有:
(1)针对现有时频分析方法不能有效分折处理瞬时频率大范围连续变化的多分量非平稳信号,以及时频聚集性不理想的问题,将多尺度的概念融合到稀疏信号分解中,研究提出了完整、系统的基于多尺度线调频基的稀疏信号分解方法,证明了该方法具有较高的时频聚集性、分解的自适应性、表示的稀疏性和较强的抗噪能力,非常适合于多分量非平稳信号的分析处理。
(2)针对转速波动情况下齿轮箱动态调制边频带难以提取的问题,研究提出了利用多尺度线调频基稀疏信号分解准确获取载波频率和调制频率曲线,从而提取齿轮箱故障特征,诊断齿轮箱故障的方法。仿真和实验分析证明了基于多尺度线调频基的稀疏信号分解方法能准确提取动态变化的调制故障特征,非常适合于转速剧烈波动情况下的齿轮箱故障诊断。
(3)针对阶比跟踪方法中转速提取困难,和基于瞬时频率的转速估计方法抗噪能力弱、精度不理想问题,研究提出利用基于多尺度线调频基的稀疏信号分解方法来提取转速信号。在齿轮箱故障诊断中的应用表明,该方法能准确提取转速信号,避免了阶比跟踪分析中转速测量设备安装困难问题,节约了诊断成本。
(4)针对广义解调方法中对频率相互不平行的多分量信号相位函数提取困难的问题,研究利用基于多尺度线调频基的稀疏信号分解方法提取多分量非平稳信号的相位函数,有效解决了广义解调方法中相位函数提取问题。对轴承故障的仿真和实验信号分析表明,利用该方法提取的相位函数对信号进行广义解调,可以将多分量非平稳信号转化为平稳信号,适用于非平稳信号的处理和变转速齿轮箱与轴承的故障诊断。
(5)为了将多个调幅调频信号线性叠加的非平稳信号分解为单个调幅调频信号,在利用基于多尺度线调频基的稀疏信号分解方法分别提取各调幅调频信号载波频率的基础上,通过对经典滤波器的扩展,研究提出滤波中心和滤波带宽可以自适应变化的时变滤波器设计方法。利用该时变滤波器可从频率成分复杂的齿轮箱振动信号中分别提取单个齿轮啮合频率调制信号,解决了转速变化下的多级传动齿轮箱存在多个啮合频率调制信号以及无关频率成分与啮合频率波动范围重叠状态下的齿轮故障诊断难题。
(6)针对多输入多输出齿轮箱传动系统和多齿轮箱系统(即一个基座安装多个齿轮箱,振动信号互相影响的系统)的振动信号中各啮合频率阶次相互干扰,从而导致故障诊断困难的问题,研究提出用基于多尺度线调频基稀疏信号分解的自适应时变滤波器逐个提取振动信号中的啮合频率调制分量,再对提取的啮合频率调制分量进行阶比分析的方法,有效抑制了其他无关联轴上齿轮啮合振动信号和其他非阶比噪声信号对阶比谱的影响,较好的解决了阶比信号相互干扰的问题,提高了阶比谱的调制识别效果,为多输入多输出齿轮箱系统和多齿轮箱系统的故障诊断提供了一条有效途径。
本文研究提出的多尺度线调频基稀疏信号分解方法融合了稀疏信号分解对基函数选择的灵活性、信号表达的简洁性以及线调频小波路径追踪算法匹配的自适应性和柔性,能有效的分解频率变化呈线性或曲线变化的多分量非平稳信号。仿真分析与应用实例表明,本文在多尺度线调频基稀疏信号分解基础上研究提出的变转速齿轮箱动态调制边频带提取、阶比跟踪转速提取、多分量非平稳信号相位函数提取以及自适应时变滤波器等方法能有效应用于变工况下的复杂齿轮箱系统的故障诊断。
Gearbox is an indispensable part for connection and power transmission in machinery, and it is vulnerable to faults as well. The research on gearbox condition monitoring and fault diagnosis is of essential importance to the safe and stability of machinery.
With features of on-line, real time, non-destructive detection, convenient, fast and accurate, gearbox’s condition monitoring and fault diagnosis based on vibration signal processing is widely used in practice. When some faults occur in gearboxes, by which the impact caused will result in various degrees and forms of modulation. How to effectively extract the sidebands from the vibration signals, which are the features of faults, is a most important part in research of gearbox fault diagnosis. Due to the difficulty of dynamic sideband extraction and the problems of traditional time frequency analysis methods, which has insufficient time-frequency gathering property, weak at noise immunity and cannot effectively analyze non-stationary signals whose instantaneous frequency varies in a large scale, the present dissertation , funded by project“Sparse Signal Decomposition Based on Multi-scale Chirplet and Its Application to Mechanical Fault Diagnosis”(Project’s Serial Number: 50875078) supported by National Natural Science Foundation of China and by project“Sparse Signal Decomposition with Amplitude Modulation Based on Multi-scale Chirplet and Its Application to Gearbox’s Fault Diagnosis”(Project’s Serial Number: 20090161110006) supported by Specialized Research Fund for the Doctoral Program of Higher Education, proposes a new signal processing method– Sparse signal Decomposition Method Based on Multi-scale Chirplet. The method is applied to the fault diagnosis of gearboxes with time-varying rotational speed. The problems such as dynamic sideband extraction of gearboxes with time-varying rotational speed, the rotational speed extraction which is needed for order tracking, the phase function extraction of multi-component non-stationary signals, and the design of self-adaptive time-varying filter are studied thoroughly. The main researches include:
(1) Due to the limitations of traditional time frequency analysis methods, which cannot effectively analyze multi-component non-stationary signals whose instantaneous frequency change continuously in a large scale and has insufficient time-frequency gathering property, the dissertation proposes a complete and systematic method denominated by Sparse Signal Decomposition Based on Multi-scale Chirplet. The method, with good time frequency gathering property, decomposition adaptively, expression sparsely and strong noise immunity, is especially suitable for the analysis of multi-component non-stationary signals.
(2) Due to the difficulty in extraction of dynamic modulation sidebands from the gearbox vibration signals under the circumstance of speed varying, the dissertation applied the Sparse Signal Decomposition Method Based on Multi-scale Chirplet to gearbox fault diagnosis, which can obtain carrier frequency and the time-varying modulation frequency accurately. Simulation and experiment prove that the method can precisely extract dynamic modulation sidebands which are the features of gearbox faults and it is especially suitable for gearbox fault diagnosis under the circumstance of drastic speed fluctuation.
(3) Due to the inadequacies in noise immunity and precision of the traditional speed extraction methods based on instantaneous frequency estimation, the dissertation uses the Sparse Signal Decomposition Method Based on Multi-scale Chirplet to estimate rotational speeds in order tracking. Its application to gearbox fault diagnosis demonstrates that the method can accurately extract rotational speed signals, avoid the installation of speed measuring equipment in order tracking analysis and save costs.
(4) In general decomposition method, it is difficult to extract phase function of multi-component non-stationary signals whose frequency curves are not parallel to each other. The present dissertation takes the advantage of Sparse Signal Decomposition Method Based on Multi-scale Chirplet to obtain phase function from multi-component non-stationary signals, which effectively solves the problem mentioned above. Simulation and application of bearing fault demonstrate that non-stationary signals can be transferred into stationary signals by using the phase function extracted by this method to carry out general decomposition, which makes it suitable to process non-stationary signals and diagnose gearbox faults under the circumstance of time-varying rotational speed.
(5) In order to separate non-stationary signals, which are the compound of AM-FM signals linear added, into single AM-FM signal, the dissertation proposes a new self-adaptively time-varying filter design method. Firstly, the carrier frequency of single AM/FM signal is extracted by the Sparse Signal Decomposition Method Based on Multi-scale Chirplet, and then, by the extension of classical filter, a self-adaptively time-varying filter is designed who’s central frequency is the carry frequency extracted. The single meshing frequency modulation signal can be filtered by the self-adaptive filter from gearbox vibration signals, which solves the problems that, under the circumstance of time-varying rotational speed, there are several meshing frequency modulation signals in multi-stage gearbox’s vibration signals, and, when the frequency of irrelevant components overlap with the meshing frequency, it is difficult to separate them and process gearbox fault diagnosis.
(6) In the fault diagnosis of multi-input and multi-output gearboxes and gearbox group (there are several gearboxes installed on one base, and the vibration signals influence each other), the orders of meshing frequency interfere with one another in the order tracking method, so it is difficult to use the order spectrum for fault diagnosis. In order to solve the problems mentioned above, a new method of fault diagnosis is proposed in the dissertation. Firstly, to extract meshing frequency modulation signals one by one with the adaptive time-varying filter using Sparse Signal Decomposition Method Based on Multi-scale Chirplet. Secondly, the order tracking is applied to the filtered signals. At last the fault diagnosis is conducted and complete. The method effectively suppresses the influences of other gear meshing vibration from unrelated transmission systems and other non-order noise signals onto order spectrum. It favorably solves the problem of order interference, and enhances order spectrum more clearly, which provides an effective method for the fault diagnosis of multi-input and multi-output gearbox and gearbox group.
The Sparse Signal Decomposition Method Based on Multi-scale Chirplet proposed by the dissertation integrates the flexibility in atom selection, the sparseness of signal expression, and matching pursuit adaptively. It can effectively decompose multi-component non-stationary signals whose frequencies change linearly or curvedly. Simulation and application examples demonstrate that, the proposed methods of the dynamic modulation sidebands extraction, time-varying rotational speed extraction, phase function extraction and adaptive time-varying filter, can be effectively applied to the fault diagnosis complex gearboxes under time-varying rotational speed condition.
基于振动信号分析处理的齿轮箱状态监测与故障诊断方法由于具有可在线、实时、非损伤、诊断便捷准确等特点,己广泛应用于工程实际。齿轮箱发生故障时,故障产生的冲击形成不同程度和形态的振动信号调制现象,如何有效的提取具有故障特征的振动信号调制边频带是齿轮箱故障诊断技术的重要研究内容。针对转速变化的复杂齿轮箱动态调制边频带难以提取和现有时频分析方法时频聚集性不够、抗噪能力弱、不能有效分析瞬时频率大范围变化的非平稳信号问题,本文在国家自然科学基金项目“多尺度线调频基稀疏信号分解方法及其在机械故障诊断中的应用研究”(项目批准号:50875078)和高等学校博士学科点专项科研基金项目“基于多尺度线调频基的稀疏信号分解包络解调方法及其在齿轮箱故障诊断中的应用研究”(项目批准号:20090161110006)资助下,研究提出了一种新的信号处理方法—多尺度线调频基稀疏信号分解方法,并将其应用于转速变化的复杂齿轮箱故障诊断,深入系统地研究了基于多尺度线调频基稀疏信号分解方法的变转速齿轮箱动态调制边频带提取、阶比跟踪转速提取、多分量非平稳信号相位函数提取以及自适应时变滤波器设计等问题,主要研究工作有:
(1)针对现有时频分析方法不能有效分折处理瞬时频率大范围连续变化的多分量非平稳信号,以及时频聚集性不理想的问题,将多尺度的概念融合到稀疏信号分解中,研究提出了完整、系统的基于多尺度线调频基的稀疏信号分解方法,证明了该方法具有较高的时频聚集性、分解的自适应性、表示的稀疏性和较强的抗噪能力,非常适合于多分量非平稳信号的分析处理。
(2)针对转速波动情况下齿轮箱动态调制边频带难以提取的问题,研究提出了利用多尺度线调频基稀疏信号分解准确获取载波频率和调制频率曲线,从而提取齿轮箱故障特征,诊断齿轮箱故障的方法。仿真和实验分析证明了基于多尺度线调频基的稀疏信号分解方法能准确提取动态变化的调制故障特征,非常适合于转速剧烈波动情况下的齿轮箱故障诊断。
(3)针对阶比跟踪方法中转速提取困难,和基于瞬时频率的转速估计方法抗噪能力弱、精度不理想问题,研究提出利用基于多尺度线调频基的稀疏信号分解方法来提取转速信号。在齿轮箱故障诊断中的应用表明,该方法能准确提取转速信号,避免了阶比跟踪分析中转速测量设备安装困难问题,节约了诊断成本。
(4)针对广义解调方法中对频率相互不平行的多分量信号相位函数提取困难的问题,研究利用基于多尺度线调频基的稀疏信号分解方法提取多分量非平稳信号的相位函数,有效解决了广义解调方法中相位函数提取问题。对轴承故障的仿真和实验信号分析表明,利用该方法提取的相位函数对信号进行广义解调,可以将多分量非平稳信号转化为平稳信号,适用于非平稳信号的处理和变转速齿轮箱与轴承的故障诊断。
(5)为了将多个调幅调频信号线性叠加的非平稳信号分解为单个调幅调频信号,在利用基于多尺度线调频基的稀疏信号分解方法分别提取各调幅调频信号载波频率的基础上,通过对经典滤波器的扩展,研究提出滤波中心和滤波带宽可以自适应变化的时变滤波器设计方法。利用该时变滤波器可从频率成分复杂的齿轮箱振动信号中分别提取单个齿轮啮合频率调制信号,解决了转速变化下的多级传动齿轮箱存在多个啮合频率调制信号以及无关频率成分与啮合频率波动范围重叠状态下的齿轮故障诊断难题。
(6)针对多输入多输出齿轮箱传动系统和多齿轮箱系统(即一个基座安装多个齿轮箱,振动信号互相影响的系统)的振动信号中各啮合频率阶次相互干扰,从而导致故障诊断困难的问题,研究提出用基于多尺度线调频基稀疏信号分解的自适应时变滤波器逐个提取振动信号中的啮合频率调制分量,再对提取的啮合频率调制分量进行阶比分析的方法,有效抑制了其他无关联轴上齿轮啮合振动信号和其他非阶比噪声信号对阶比谱的影响,较好的解决了阶比信号相互干扰的问题,提高了阶比谱的调制识别效果,为多输入多输出齿轮箱系统和多齿轮箱系统的故障诊断提供了一条有效途径。
本文研究提出的多尺度线调频基稀疏信号分解方法融合了稀疏信号分解对基函数选择的灵活性、信号表达的简洁性以及线调频小波路径追踪算法匹配的自适应性和柔性,能有效的分解频率变化呈线性或曲线变化的多分量非平稳信号。仿真分析与应用实例表明,本文在多尺度线调频基稀疏信号分解基础上研究提出的变转速齿轮箱动态调制边频带提取、阶比跟踪转速提取、多分量非平稳信号相位函数提取以及自适应时变滤波器等方法能有效应用于变工况下的复杂齿轮箱系统的故障诊断。
Gearbox is an indispensable part for connection and power transmission in machinery, and it is vulnerable to faults as well. The research on gearbox condition monitoring and fault diagnosis is of essential importance to the safe and stability of machinery.
With features of on-line, real time, non-destructive detection, convenient, fast and accurate, gearbox’s condition monitoring and fault diagnosis based on vibration signal processing is widely used in practice. When some faults occur in gearboxes, by which the impact caused will result in various degrees and forms of modulation. How to effectively extract the sidebands from the vibration signals, which are the features of faults, is a most important part in research of gearbox fault diagnosis. Due to the difficulty of dynamic sideband extraction and the problems of traditional time frequency analysis methods, which has insufficient time-frequency gathering property, weak at noise immunity and cannot effectively analyze non-stationary signals whose instantaneous frequency varies in a large scale, the present dissertation , funded by project“Sparse Signal Decomposition Based on Multi-scale Chirplet and Its Application to Mechanical Fault Diagnosis”(Project’s Serial Number: 50875078) supported by National Natural Science Foundation of China and by project“Sparse Signal Decomposition with Amplitude Modulation Based on Multi-scale Chirplet and Its Application to Gearbox’s Fault Diagnosis”(Project’s Serial Number: 20090161110006) supported by Specialized Research Fund for the Doctoral Program of Higher Education, proposes a new signal processing method– Sparse signal Decomposition Method Based on Multi-scale Chirplet. The method is applied to the fault diagnosis of gearboxes with time-varying rotational speed. The problems such as dynamic sideband extraction of gearboxes with time-varying rotational speed, the rotational speed extraction which is needed for order tracking, the phase function extraction of multi-component non-stationary signals, and the design of self-adaptive time-varying filter are studied thoroughly. The main researches include:
(1) Due to the limitations of traditional time frequency analysis methods, which cannot effectively analyze multi-component non-stationary signals whose instantaneous frequency change continuously in a large scale and has insufficient time-frequency gathering property, the dissertation proposes a complete and systematic method denominated by Sparse Signal Decomposition Based on Multi-scale Chirplet. The method, with good time frequency gathering property, decomposition adaptively, expression sparsely and strong noise immunity, is especially suitable for the analysis of multi-component non-stationary signals.
(2) Due to the difficulty in extraction of dynamic modulation sidebands from the gearbox vibration signals under the circumstance of speed varying, the dissertation applied the Sparse Signal Decomposition Method Based on Multi-scale Chirplet to gearbox fault diagnosis, which can obtain carrier frequency and the time-varying modulation frequency accurately. Simulation and experiment prove that the method can precisely extract dynamic modulation sidebands which are the features of gearbox faults and it is especially suitable for gearbox fault diagnosis under the circumstance of drastic speed fluctuation.
(3) Due to the inadequacies in noise immunity and precision of the traditional speed extraction methods based on instantaneous frequency estimation, the dissertation uses the Sparse Signal Decomposition Method Based on Multi-scale Chirplet to estimate rotational speeds in order tracking. Its application to gearbox fault diagnosis demonstrates that the method can accurately extract rotational speed signals, avoid the installation of speed measuring equipment in order tracking analysis and save costs.
(4) In general decomposition method, it is difficult to extract phase function of multi-component non-stationary signals whose frequency curves are not parallel to each other. The present dissertation takes the advantage of Sparse Signal Decomposition Method Based on Multi-scale Chirplet to obtain phase function from multi-component non-stationary signals, which effectively solves the problem mentioned above. Simulation and application of bearing fault demonstrate that non-stationary signals can be transferred into stationary signals by using the phase function extracted by this method to carry out general decomposition, which makes it suitable to process non-stationary signals and diagnose gearbox faults under the circumstance of time-varying rotational speed.
(5) In order to separate non-stationary signals, which are the compound of AM-FM signals linear added, into single AM-FM signal, the dissertation proposes a new self-adaptively time-varying filter design method. Firstly, the carrier frequency of single AM/FM signal is extracted by the Sparse Signal Decomposition Method Based on Multi-scale Chirplet, and then, by the extension of classical filter, a self-adaptively time-varying filter is designed who’s central frequency is the carry frequency extracted. The single meshing frequency modulation signal can be filtered by the self-adaptive filter from gearbox vibration signals, which solves the problems that, under the circumstance of time-varying rotational speed, there are several meshing frequency modulation signals in multi-stage gearbox’s vibration signals, and, when the frequency of irrelevant components overlap with the meshing frequency, it is difficult to separate them and process gearbox fault diagnosis.
(6) In the fault diagnosis of multi-input and multi-output gearboxes and gearbox group (there are several gearboxes installed on one base, and the vibration signals influence each other), the orders of meshing frequency interfere with one another in the order tracking method, so it is difficult to use the order spectrum for fault diagnosis. In order to solve the problems mentioned above, a new method of fault diagnosis is proposed in the dissertation. Firstly, to extract meshing frequency modulation signals one by one with the adaptive time-varying filter using Sparse Signal Decomposition Method Based on Multi-scale Chirplet. Secondly, the order tracking is applied to the filtered signals. At last the fault diagnosis is conducted and complete. The method effectively suppresses the influences of other gear meshing vibration from unrelated transmission systems and other non-order noise signals onto order spectrum. It favorably solves the problem of order interference, and enhances order spectrum more clearly, which provides an effective method for the fault diagnosis of multi-input and multi-output gearbox and gearbox group.
The Sparse Signal Decomposition Method Based on Multi-scale Chirplet proposed by the dissertation integrates the flexibility in atom selection, the sparseness of signal expression, and matching pursuit adaptively. It can effectively decompose multi-component non-stationary signals whose frequencies change linearly or curvedly. Simulation and application examples demonstrate that, the proposed methods of the dynamic modulation sidebands extraction, time-varying rotational speed extraction, phase function extraction and adaptive time-varying filter, can be effectively applied to the fault diagnosis complex gearboxes under time-varying rotational speed condition.
引文
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[22] Zhou R,Bao W,Li N, et al.Mechanical equipment fault diagnosis based on redundant second generation wavelet packet transform.Digital Signal Processing, 2010,20(1):276-288
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[25] Ting L K,Cowan C F N,Woods R F. LMS coefficient filtering for Time-varying chirped signals.IEEE Transactions on Signal Processing, 2004, 52(11): 3160 -3169
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[30] Ye J J,He Y M,Chen X F, et al.Pipe crack identification based on finite element method of second generation wavelets.Mechanical Systems and Signal Processing,2010,24(2): 379-393
[31] Flandrin P,Rilling G,Goncalves P.Empirical Mode Decomposition as a Filter Bank.IEEE Signal Processing Letters,2004,11(2):112-114
[32] Jiang H K,He Z J,Duan C D, et al.Gearbox fault diagnosis using adaptive redundant Lifting Scheme Mechanical Systems and Signal Processing, 2006, 20(8): 1992-2006
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[35] Zhan Y M,Makis V,Jardine A K S.A robust diagnostic model for gearboxes subject to vibration monitoring.Journal of Sound and Vibration, 2006, 290(3-5): 928-955
[36] Zhan Y M,Mechefske C K.Robust detection of gearbox deterioration using compromised autoregressive modeling and Kolmogorov-Smirnov test statistic Part I:Compromised autoregressive modeling with the aid of hypothesis tests and simulation analysis.Mechanical Systems and Signal Processing, 2007, 21(5): 1953-1982
[37] Zhan Y M,Makis V,Jardine A K S.Adaptive state detection of gearboxes under varying load conditions based on parametric modelling.Mechanical Systems and Signal Processing,2006,20(1):188-221
[38] Wang X Y,Makis V.Autoregressive model-based gear shaft fault diagnosis using the Kolmogorov-Smirnov test.Journal of Sound and Vibration, 2009, 327(3-5): 413-423
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[40]于德介,程军圣,杨宇.机械故障诊断的Hilbert-Huang变换方法.北京:科学出版社,2006,24-34
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[42] Fyfe K R,Munck E D S.Analysis of computed order tracking Mechanical System and Signal Processing,1997,11(2):187-205
[43] Bossley K M,Mckendrick R J.Hybrid computed order tracking.Mechanical System and Signal Processing,1999,13(4):627-641
[44]郭瑜,秦树人,汤宝平,等.基于瞬时频率估计的旋转机械阶比跟踪.机械工程学报,2003,39(3):32-36
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[47] Wu J D,Huang C W,Huang R W.An application of a recursive Kalman filtering algorithm in rotating machinery fault diagnosis.NDT&E International, 2004, 37(5):411-419
[48] Pan M C,Liao S W,Chiu C C.Improvement on Gabor order tracking and objective comparison with Vold-Kalman filtering order tracking.Mechanical Systems and Signal Processing,2007,21(2):653-667
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