随着“工业4.0”和“中国制造2025”战略的提出，全球范围内对智能制造与高端装备制造业的转型升级给予了高度重视。在此背景下，行星齿轮传动系统的维护和故障诊断技术成为保障设备安全高效运行的关键。有效的故障特征提取方法和准确的诊断技术对提升行星齿轮传动系统维修效率及完好率具有至关重要的意义。

本文综合探讨了变转速行星轮系振动信号特征提取与故障诊断方法，聚焦于分数阶傅里叶变换（Fractional Fourier Transform，FRFT）和迭代奇异值分解算法（Iterative Singular Value Decomposition，ISVD）的理论研究及其在实际应用中的实效性验证。针对行星齿轮传动系统，首先分析了齿轮故障的机理，包括断齿、点蚀、磨损等典型故障形式及其对系统性能的影响。通过构建数学模型，详细讨论了齿轮啮合频率及其谐波成分在变转速工况下的变化规律以及调制效应产生的边带对故障诊断的重要性，为故障的精确诊断提供了理论基础。

针对变转速行星轮系太阳轮故障特征提取问题，详细探讨了基于FRFT的滤波原理及其在变转速行星轮系故障诊断中的应用，包括包络分析和最佳FRFT阶次的确定方法。通过一系列的仿真和实验验证，证明了该方法在分析行星轮系故障信号方面的有效性。这些验证覆盖了多种工况，包括高转速时的高负载和低负载条件，以及低转速时的高负载和低负载条件，为该方法的推广应用提供了实验支持。实验结果显示，所提方法能够准确提取故障特征阶次，证明了其在工程实践中的可行性和准确性。

针对变转速行星轮系太阳轮故障特征提取问题，还详细探讨了奇异值分解（Singular Value Decomposition，SVD）的基本原理及其在信号降噪中的应用。提出了通过ISVD来提取行星轮系在变转速工况下故障特征的方法，包括小波包变换谱峭度、ISVD降噪以及信号重构技术。通过仿真与实验验证，对比了经验模态分解（Empirical Mode Decomposition，EMD）和变分模态分解（Variational Modal Decomposition，VMD），证明了ISVD方法在分析行星轮系故障信号方面的有效性和优越性。实验涵盖了齿根裂纹、局部断齿、整体断齿等不同类型故障，以及正常齿轮。证明了所提方法在提高信噪比和准确提取故障特征方面具有一定优势。

针对变转速行星轮系太阳轮在线故障诊断的挑战，将基于FRFT和ISVD算法的诊断方法应用于嵌入式设备。设计了一个在线故障诊断系统的硬件框架，包括信号采集模块和处理模块，采用STM32H743微控制器作为核心处理单元，实现了高效的数据采集和处理。将FRFT和ISVD算法从MATLAB环境转换为C++代码，实现了这些算法在嵌入式设备上的在线运行，有效提升了故障诊断能力。实验表明，所提方法能够准确提取变转速行星轮系的太阳轮故障特征，在线地完成故障诊断，证明了其在实际应用中的有效性。通过程序开发，成功地将复杂的信号处理算法迁移到嵌入式系统中，不仅保证了算法的性能，还增强了系统在线监测和故障诊断的准确性。

综上所述，本文不仅在理论上为变转速行星轮系故障诊断提供了新的技术路径，而且在实践中通过嵌入式设备实现了在线故障诊断系统布署，展现了其在工程实际应用中的实用价值，对推动行星轮系故障诊断技术发展具有重要的理论和实践意义。

With the strategy of "Industry 4.0" and "Made in China 2025" put forward, great attention has been paid to the transformation and upgrading of intelligent manufacturing and high-end equipment manufacturing worldwide. In this context, the maintenance and fault diagnosis technology of planetary gear transmission system has become the key to ensure the safe and efficient operation of equipment. Effective fault feature extraction method and accurate diagnosis technology are of great significance to improve the maintenance efficiency and intact rate of planetary gear transmission system.

In this thesis, the methods of vibration signal feature extraction and fault diagnosis of variable-speed planetary gear trains are comprehensively discussed, focusing on the theoretical research of Fractional Fourier Transform (FRFT) and iterative singular value decomposition (ISVD) and their effectiveness verification in practical applications. Aiming at planetary gear transmission system, firstly, the mechanism of gear failure is analyzed, including typical failure forms such as broken teeth, pitting corrosion and wear, and their effects on system performance. By constructing a mathematical model, the variation law of gear meshing frequency and its harmonic components under the condition of variable speed and the importance of sideband produced by modulation effect to fault diagnosis are discussed in detail, which provides a theoretical basis for accurate fault diagnosis.

Aiming at the problem of sun gear fault feature extraction of variable speed planetary gear train, the filtering principle based on FRFT and its application in fault diagnosis of variable speed planetary gear train are discussed in detail, including envelope analysis and the method of determining the best FRFT order. Through a series of simulations and experiments, it is proved that this method is effective in analyzing the fault signals of planetary gear trains. These verifications cover a variety of working conditions, including high load and low load conditions at high speed and high load and low load conditions at low speed, which provide experimental support for the popularization and application of this method. The experimental results show that the proposed method can accurately extract the fault feature order, which proves its feasibility and accuracy in engineering practice.

Aiming at the problem of sun gear fault feature extraction of variable speed planetary gear train, the basic principle of Singular Value Decomposition (SVD) and its application in signal denoising are also discussed in detail. A method to extract the fault characteristics of planetary gear train under variable speed by ISVD is proposed, including wavelet packet transform spectral kurtosis, ISVD noise reduction and signal reconstruction technology. Through simulation and experimental verification, Empirical Mode Decomposition (EMD) and Variational Modal Decomposition (VMD) are compared, which proves the effectiveness and superiority of ISVD method in analyzing fault signals of planetary gear trains. The experiment covers different types of faults, such as root crack, partial broken teeth, whole broken teeth and normal gears. It is proved that the proposed method has certain advantages in improving signal-to-noise ratio and accurately extracting fault features.

Aiming at the challenge of online fault diagnosis for sun gear of variable speed planetary gear train, the diagnosis method based on FRFT and ISVD algorithm is applied to embedded equipment. The hardware framework of an online fault diagnosis system is designed, including signal acquisition module and processing module. With STM32H743 microcontroller as the core processing unit, efficient data acquisition and processing are realized. The FRFT and ISVD algorithms are converted from MATLAB environment to C++ code, which realizes the online operation of these algorithms on embedded devices and effectively improves the fault diagnosis ability. Experiments show that the proposed method can accurately extract the sun gear fault characteristics of the planetary gear train with variable speed and complete the fault diagnosis online, which proves its effectiveness in practical application. Through program development, the complex signal processing algorithm is successfully migrated to the embedded system, which not only ensures the performance of the algorithm, but also enhances the accuracy of online monitoring and fault diagnosis of the system.

In summary, this thesis not only provides a new theoretical approach for fault diagnosis in variable speed planetary gear systems but also demonstrates practical value through the deployment of an online fault diagnosis system on embedded devices in real-world applications, significantly advancing the development of fault diagnosis technologies in theory and practice.

[1]张曙. 工业4.0和智能制造[J]. 机械设计与制造工程, 2014, 43(08): 1-5.

[2]周济. 智能制造——“中国制造2025”的主攻方向[J]. 中国机械工程, 2015, 26(17): 2273-2284.

[3]吴鲁纪, 耿福震. 高速齿轮传动技术与装置综述[J]. 机械传动, 2019, 43(11): 172-175.

[4]王延忠, 赵鹏坤, 李圆, 等. 双内啮合行星齿轮传动设计与试验研究[J]. 机械传动, 2017, 41(10): 146-151.

[5]秦波, 尹恒, 王卓, 等. EMPE和KP-KELM在行星齿轮箱故障诊断中的应用[J]. 机械传动, 2019, 43(05): 146-151.

[6]雷亚国, 何正嘉, 林京, 等. 行星齿轮箱故障诊断技术的研究进展[J]. 机械工程学报, 2011, 47 (19): 59-67.

[7]程亮, 张步勤, 张金营. 基于IGWO优化LSSVM的采煤机截割部齿轮箱故障诊断[J]. 煤矿机械, 2021, 42(05): 168-171.

[8]吴守军, 冯辅周, 吴春志, 等. 基于VMD-DE的坦克行星变速箱故障诊断方法研究[J]. 振动与冲击, 2020, 39(10): 170-179.

[9]Y. Tian, J. Ma, C. Lu, et al. Rolling bearing fault diagnosis under variable conditions using LMD-SVD and extreme learning machine[J]. Mechanism and Machine Theory, 2015, 90: 175-186.

[10]X. Zhao, B. Ye. Singular value decomposition packet and its application to extraction of weak fault feature[J]. Mechanical Systems and Signal Processing, 2016, 70-71: 73-86.

[11]涂福泉, 杨家瑜, 陈超, 等. 基于DMD降噪的滚动轴承故障诊断方法[J]. 武汉科技大学学报, 2023, 46(05): 376-383.

[12]张亦伟, 周邵萍, 王伟, 等. 基于SSA-SVD降噪和卷积神经网络的行星齿轮箱故障诊断研究[J]. 化工设备与管道, 2023, 60(01): 55-62.

[13]霍爱清, 王泽文, 胥静蓉, 等. 井下指令信号的小波-奇异值分解双层滤波降噪[J]. 西安石油大学学报(自然科学版), 2023, 38(03): 100-105.

[14]C. Yi, Y. Lv, H. Xiao, et al. Multisensor signal denoising based on matching synchro squeezing wavelet transform for mechanical fault condition assessment[J]. Measurement Science and Technology, 2018, 29(04): 45104.

[15]R. Wiggins. Minimum entropy deconvolution[J]. Geoexploration, 1978, 16(1-2): 21-35.

[16]崔屹. 图像处理与分析数学形态学方法及应用[M]. 科学出版社, 2000.

[17]Y. Lei, J. Lin, Z. He, et al. Application of an improved kurtogram method for fault diagnosis of rolling element bearings[J]. Mechanical Systems and Signal Processing, 2011, 25(05): 1738-1749.

[18]T. Barszcz, A. JabLonski. A novel method for the optimal band selection for vibration signal demodulation and comparison with the kurtogram[J]. Mechanical Systems and Signal Processing, 2011, 25(01): 431-451.

[19]G. McDonald, Q. Zhao, M. Zuo. Maximum correlated kurtosis deconvolution and application on gear tooth chip fault detection[J]. Mechanical Systems and Signal Processing, 2012, 33: 237-255.

[20]陈鑫, 郭瑜. 平均降采样多周期微分均值的旋转部件故障特征增强方法[J]. 振动工程学报, 2024, 37(02): 346-355.

[21]谯自健, 陈帅, 马莉, 等. 多稳态匹配随机共振在机械早期故障特征提取中的应用[J]. 振动与冲击, 2023, 42(11): 87-95.

[22]S. Lu, Q. He, J. Wang. A review of stochastic resonance in rotating machine fault detection[J]. Mechanical Systems and Signal Processing, 2019, 116: 230-260.

[23]尹玉玺, 周常飞, 史春祥, 等. 采煤机摇臂齿轮箱故障诊断研究现状及展望[J]. 煤炭工程, 2022, 54(11): 107-112.

[24]陈哲明, 王理章, 喻洋. 考虑传动系统扭转振动的单节列车动力学特性分析[J]. 机械传动, 2016, 40(10): 122-126.

[25]张立军, 朱文栋. 基于纯扭转模型的行星齿轮系统固有振动特性仿真分析[C]//2013中国汽车工程学会年会, 北京, 中国, 2013, 890-893.

[26]黄毅. 车辆传动系统非线性振动响应灵敏度与动力学修改研究[D]. 北京: 北京理工大学, 2015.

[27]高玉才, 付忠广, 谢玉存, 等. 基于教师-学生网络的半监督故障诊断模型[J]. 振动与冲击, 2024, 43(04): 150-157.

[28]李从跃, 胡以怀, 沈威, 等. 基于小波变换和CNN的船用机械故障诊断[J]. 中国测试, 2024, 50(03): 183-192.

[29]N. Huang, Z. Shen, S. Lon, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proceedings: Mathematical, Physical and Engineering Sciences, 1998, 454: 903-995.

[30]J. Yan, L. Lu. Improved Hilbert Huang transform based weak signal detection methodology and its application on incipient fault diagnosis and ECG signal analysis[J]. Signal Processing, 2014, 98: 74-87.

[31]隋文涛, 张丹,W. Wilson, 等. 基于EMD和MKD的滚动轴承故障诊断方法[J]. 振动与冲击, 2015, 34(09): 55-59+64.

[32]陈俊洵, 程龙生, 胡绍林了, 等. 基于EMD的改进马田系统的滚动轴承故障诊断[J]. 振动与冲击, 2017, 36(05): 151-156.

[33]R. Ma, Y. Chen, H. Sun. Detection of weak signals based on empirical mode decomposition and singular spectrum analysis[J]. IET Signal Processing, 2013, 7(4): 269-276.

[34]潘宏侠, 张玉学. 基于SST时频图纹理特征的供输弹系统故障诊断[J]. 振动与冲击, 2020, 39(06): 132-137+175.

[35]陈焱, 郑近德, 潘海洋, 等. 复合多尺度反向散布熵在轴承故障诊断中的应用[J]. 振动与冲击, 2022, 41(19): 55-63.

[36]潘海洋, 郑近德, 童宝宏, 等. 基于稀疏带宽模态分解的变转速滚动轴承故障诊断[J]. 振动与冲击, 2017, 36(14): 92-97.

[37]武英杰, 辛红伟, 王建国, 等. 基于VMD滤波和极值点包络阶次的滚动轴承故障诊断[J]. 振动与冲击, 2018, 37(14): 102-107.

[38]包文杰, 涂晓彤, 李富才, 等. 参数化的短时傅里叶变换及齿轮箱故障诊断[J]. 振动.测试与诊断, 2020, 40(02): 272-277+417.

[39]毛清华, 张勇强, 赵晓勇, 等. 变速工况下采煤机行星齿轮传动系统故障诊断[J]. 工矿自动化, 2021, 47(07): 8-13.

[40]M. Kutay, H. Ozaltas, O. Arikan, et al. Optimal filtering in fractional Fourier domains [J]. IEEE Transactions on Signal Processing, 1997, 45(5): 1129-1143.

[41]S. Sharrma, R. Saxena, S. Saxena. Tuning of FIR filter transition bandwidth using fractional Fourier transform[J]. Signal Processing, 2007, 87(12): 3147-3154.

[42]梅检民, 肖云魁, 杨万成, 等. 基于分数阶傅里叶变换的邻近阶比分离研究[J]. 振动与冲击, 2012, 31(11): 38-41+53.

[43]温广瑞, 杜小伟, 张志芬, 等. FRFT在转子起停车状态评估中的应用研究进展[J]. 振动.测试与诊断, 2016, 36(05): 821-828+1018.

[44]黄铭, 郑永军, 汪洋百慧. 基于分数阶傅里叶滤波的电动助力器故障检测[J]. 振动与冲击, 2020, 39(23): 263-270.

[45]梅检民, 常春, 沈虹, 等. 基于分数阶滤波的全息阶比解调谱及齿轮早期故障诊断[J].振动与冲击, 2023, 42(10): 273-277+288.

[46]施巍松, 孙辉, 曹杰, 等. 边缘计算:万物互联时代新型计算模型[J]. 计算机研究与发展, 2017, 54(05): 907-924.

[47]张琪, 胡宇鹏, 嵇存, 等. 边缘计算应用:传感数据异常实时检测算法[J]. 计算机研究与发展, 2018, 55(03): 524-536.

[48]李子姝, 谢人超, 孙礼, 等. 移动边缘计算综述[J]. 电信科学, 2018, 34(01): 87-101.

[49]伊平. 物联网技术发展和应用的信息安全及伦理问题研究[D]. 锦州: 渤海大学, 2018.

[50]胡宝玲, 王彦贞, 陈淑春. 物联网技术在智能家居系统中的应用[J]. 集成电路应用, 2022, 39(06): 160-161.

[51]侯瑞春, 丁香乾, 陶冶, 等. 制造物联及相关技术架构研究[J]. 计算机集成制造系统, 2014, 20(01): 11-20.

[52]徐镇. 基于边缘智能的数控装备故障诊断系统的设计与实现[D]. 北京: 中国科学院大学, 2022.

[53]汤华松.基于边缘计算的电机轴承故障诊断方法研究[D]. 合肥: 安徽大学, 2021.

[54]S. Lu, P. Zhou, X. Wang, et al. Condition monitoring and fault diagnosis of motor bearings using undersampled vibration signals from a wireless sensor network[J]. Journal of Sound & Vibration, 2017, 414: 81-96.

[55]D. Park, S. Kim, Y. An, et al. LiReD: A Light-Weight Real-Time Fault Detection System for Edge Computing Using LSTM Recurrent Neural Networks[J]. Sensors, 2018, 18(7): 2110-2124.

[56]F. Chen, Z. Fu, Z. Yang. Wind power generation fault diagnosis based on deep learning model in internet of things (IoT) with clusters[J]. Cluster Computing, 2018, 22(6): 14013-14025.

[57]武向军, 李海虹, 郭宏. 基于边缘计算的滚动轴承智能监测系统研究[J]. 太原科技大学学报, 2023, 44(03): 252-257.

[58]吴启航, 丁晓喜, 何清波, 黄文彬. 齿轮箱故障边缘智能诊断方法及应用研究[J]. 仪器仪表学报, 2024, 45(01): 70-80.

[59]任勇. 变转速旋转机械关键零部件故障诊断研究[D]. 江苏：中国矿业大学, 2019.

[60]盛兆顺, 尹琦岭. 设备状态监测与故障诊断技术及应用[M]. 北京: 化学工业出版社, 2003.

[61]吕蓬. 旋转机械故障模式识别方法研究[D]. 北京: 华北电力大学, 2010.

[62]丁康, 李巍华, 朱小勇, 等. 齿轮及齿轮箱故障诊断实用技术[M]. 北京: 机械工业出版社, 2005.

[63]G. He, K. Ding, W. Li, et al. A novel order tracking method for wind turbine planetary gearbox vibration analysis based on discrete spectrum correction technique[J]. Renewable Energy, 2016, 87(1): 364-375.

[64]R. Pootter. A new order tracking method for rotating machinery[J]. Sound and Vibration, 1990,24(9): 30-34.

[65]陶然, 邓兵, 王越. 分数阶傅里叶变换及其应用[M]. 北京: 清华大学出版社, 2009.

[66]H. Ozaktas, Z. Zalevsky, M. Kutay. The Fractional Fourier Transform: with Applications in Optics and Signal Processing[M]. New York: Wiley, 2001.

[67]S. Pei, J. Ding. Closed-form discrete fractional and affine Fourier transforms[J]. IEEE Transactions on Signal Processing, 2000,48(5): 1338-1353.

[68]S. Pei, M. Yeh. Improved discrete fractional Fourier transform[J]. Optics Letters, 1997, 22(14):1047-1049.

[69]B. Santhanam, J. McClellan. The discrete rotational Fourier transform[J]. IEEE Transactions on Signal Processing, 1996, 44(4): 994-998.

[70]马金铭, 苗红霞, 苏新华, 等. 分数傅里叶变换理论及其应用研究进展[J]. 光电工程, 2018, 45(06): 5-28.

[71]从飞云. 基于滑移向量序列奇异值分解的滚动轴承故障诊断研究[D]. 上海: 上海交通大学, 2012.

[72]刘献栋, 杨绍普, 申永军, 等. 基于奇异值分解的突变信息检测新方法及其应用[J]. 机械工程学报, 2002(06): 102-105.

[73]陈恩利, 吴勇军, 申永军, 等. 基于改进奇异值分解技术的齿轮调制故障特征提取[J]. 振动工程学报, 2008(05): 530-534.

[74]赵学智, 叶邦彦, 陈统坚. 矩阵构造对奇异值分解信号处理效果的影响[J]. 华南理工大学学报(自然科学版), 2008, 36(09): 86-93.

[75]高成文, 孙云鹏. 基于hankel矩阵奇异值分解的速变参数去噪方法实现及仿真分析[J].遥测遥控, 2014, 35(01): 60-64.

[76]江帆. 矿井提升机主轴装置故障诊断方法研究[D]. 徐州: 中国矿业大学, 2015.

[77]赵学智, 叶邦彦, 陈统坚. 奇异值差分谱理论及其在车床主轴箱故障诊断中的应用[J].机械工程学报, 2010,46(01): 100-108.

[78]杨文献, 任兴民, 姜节胜. 基于奇异熵的信号降噪技术研究[J]. 西北工业大学学报, 2001(03): 368-371.

[79]P. Comon, G. Golub. Tracking a few extreme singular values and vectors in signal processing[J]. Proceedings of the IEEE, 1990, 78(8) : 1327-1343.

[80]D. Bianchi, E. Mayrhofer, M. Groeschl, et al. Wavelet packet transform for detection of single events in acoustic emission signals[J]. Mechanical Systems and Signal Processing, 2015,64–65: 441-451.