610 工程科学学报，第39卷，第4期 号的分析结果.在Fourier频谱如图7(b)中，电动机转 Vold-Kalman filter and higher order energy separation for fault di- 频的初始频率60Hz处出现了明显的峰值，但同样无 agnosis of wind turbine planetary gearbox under nonstationary con- 法判断齿轮箱工作正常与否.STFT和IG-STFT的分析 ditions.Reneuable Energy,2016,85:45 结果如图7(c)和(d)所示.可见时频图中的主导频率 [5]Li C.Liang M.Time-frequency signal analysis for gearbox fault diagnosis using a generalized synchrosqueezing transform.Mech 依次为第二级行星齿轮箱齿轮啮合频率∫、太阳轮故 Syst Signal Process,2012,26:205 障特征频率∫2及转频的组合频率：fe+2f。- [6]Hlawatsch F,Boudreaux-Bartels G.Linear and quadratic time- 38-2f2及电动机转频∫：由于上述频率成分与第二 frequency signal representations.IEEE Signal Process Mag, 级行星齿轮箱太阳轮相关，故判定第二级行星齿轮箱 1992,9(2):21 太阳轮出现故障，与实际情况相符 ]Cohen L Time-frequeney distributions:a review.Proc IEEE, 1989,77(7):941 4结论 [8]Chen X W,Feng Z P,Liang M.Planetary gearbox fault diagnosis under timevariant conditions based on iterative generalized syn- 本文在充分发挥ST℉T和广义解调优势的基础 chrosqueezing transform.J Mech Eng,2015,51(1)131 上，运用迭代广义解调对STT进行了改造，提出了迭 (陈小旺，冯志鹏，山ANG Ming.基于迭代广义同步压缩变换 代广义短时Fourier变换，达到在分析非平稳信号的过 的时变工祝行星齿轮箱故障诊断.机械工程学报，2015,51 程中得到能量聚集性很好的时频分布的目的.最后， (1):131) 运用迭代广义短时Fourier变换分析了行星齿轮箱太 9]Martin W,Flandrin P.Wigner-Ville spectral analysis of nonsta- tionary processes.IEEE Trans Acoust Speech Signal Process, 阳轮故障仿真信号及实验信号，分析结果表明该方法 1985,33(6):1461 可以准确刻画非平稳信号的时变特征和诊断齿轮故 [10]Yu G,Zhou Y Q.General linear chirplet transform.Mech Syst 障，验证了所提出方法的有效性 Signal Process,2016,70:958 [11]Cheng J S,Yang Y,Yu D J.The envelope order speetrum based 参考文献 on generalized demodulation time-frequency analysis and its ap- plication to gear fault diagnosis.Mech Syst Signal Process,2010, [1]Tian SS,Qian Z.Planetary gearbox fault feature enhancement 24(2):508 based on combined adaptive filter method.Adr Mech Eng,2015, 12]Li C,Liu Z X,Zhou F X,et al.Application of generalized de- 7(12):1 modulation in bearing fault diagnosis of inverter fed induction mo- 2]Lei Y G,He Z J,Lin J,et al.Research advances of fault diagno- tors /Proceeding of the 11th World Congress on Intelligent Con- sis technique for planetary gearboxes.J Mech Eng,2011,47 trol and Automation IEEE.Shenyang,2014:2328 (19):59 3] Wang Y,Xu G H,Luo A L,et al.An online tacholess order (雷亚国，何正嘉，林京，等.行星齿轮箱故障诊断技术的研 tracking technique based on generalized demodulation for rolling 究进展.机械工程学报，2011,47(19)：59) bearing fault detection.J Sound Vib,2016,367:233 3]Feng Z P,Fan YX,Liang M,et al.A nonstationary vibration [14]Olhede S,Walden A T.A generalized demodulation approach to signal analysis method for fault diagnosis of planetary gearboxes time-frequency projections for multicomponent signals.Proc Proc CSEE,2013,33(17):105 Math Phys Eng Sci,2005,461(2059):2159 (冯志鹏，范寅夕，LIANG Ming,等.行星齿轮箱故障诊断的 [15]Cheng J S,Yang Y,Yu D J.Application of the improved gener- 非平稳振动信号分析方法.中国电机工程学报，2013,33 alized demodulation time-frequency analysis method to multi- (17):105) component signal decomposition.Signal Process,2009,89(6): 4]Feng Z P,Qin S F,Liang M.Time-frequeney analysis based on 1205工程科学学报，第 39 卷，第 4 期 号的分析结果． 在 Fourier 频谱如图 7( b) 中，电动机转 频的初始频率 60 Hz 处出现了明显的峰值，但同样无 法判断齿轮箱工作正常与否． STFT 和 IG-STFT 的分析 结果如图 7( c) 和( d) 所示． 可见时频图中的主导频率 依次为第二级行星齿轮箱齿轮啮合频率 fm2、太阳轮故 障特征频率 fs2 及转频 f ( r) s2 的组合频率: fm2 + 2fs2、fm2 － 3f ( r) s2 － 2fs2及电动机转频 fd ． 由于上述频率成分与第二 级行星齿轮箱太阳轮相关，故判定第二级行星齿轮箱 太阳轮出现故障，与实际情况相符． 4 结论 本文在充分发挥 STFT 和广义解调优势的基础 上，运用迭代广义解调对 STFT 进行了改造，提出了迭 代广义短时 Fourier 变换，达到在分析非平稳信号的过 程中得到能量聚集性很好的时频分布的目的． 最后， 运用迭代广义短时 Fourier 变换分析了行星齿轮箱太 阳轮故障仿真信号及实验信号，分析结果表明该方法 可以准确刻画非平稳信号的时变特征和诊断齿轮故 障，验证了所提出方法的有效性． 参 考 文 献 ［1］ Tian S S，Qian Z． Planetary gearbox fault feature enhancement based on combined adaptive filter method． Adv Mech Eng，2015， 7( 12) : 1 ［2］ Lei Y G，He Z J，Lin J，et al． Ｒesearch advances of fault diagno￾sis technique for planetary gearboxes． J Mech Eng，2011，47 ( 19) : 59 ( 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． 机械工程学报，2011，47( 19) : 59) ［3］ Feng Z P，Fan Y X，Liang M，et al． A nonstationary vibration signal analysis method for fault diagnosis of planetary gearboxes． Proc CSEE，2013，33( 17) : 105 ( 冯志鹏，范寅夕，LIANG Ming，等． 行星齿轮箱故障诊断的 非平稳振动信号分析方法． 中 国 电 机 工 程 学 报，2013，33 ( 17) : 105) ［4］ Feng Z P，Qin S F，Liang M． Time--frequency analysis based on Vold-Kalman filter and higher order energy separation for fault di￾agnosis of wind turbine planetary gearbox under nonstationary con￾ditions． Ｒenewable Energy，2016，85: 45 ［5］ Li C，Liang M． Time--frequency signal analysis for gearbox fault diagnosis using a generalized synchrosqueezing transform． Mech Syst Signal Process，2012，26: 205 ［6］ Hlawatsch F，Boudreaux-Bartels G． Linear and quadratic time-- frequency signal representations． IEEE Signal Process Mag， 1992，9( 2) : 21 ［7］ Cohen L． Time--frequency distributions: a review． Proc IEEE， 1989，77( 7) : 941 ［8］ Chen X W，Feng Z P，Liang M． Planetary gearbox fault diagnosis under time-variant conditions based on iterative generalized syn￾chrosqueezing transform． J Mech Eng，2015，51( 1) : 131 ( 陈小旺，冯志鹏，LIANG Ming． 基于迭代广义同步压缩变换 的时变工况行星齿轮箱故障诊断． 机械工程学报，2015，51 ( 1) : 131) ［9］ Martin W，Flandrin P． Wigner-Ville spectral analysis of nonsta￾tionary processes． IEEE Trans Acoust Speech Signal Process， 1985，33( 6) : 1461 ［10］ Yu G，Zhou Y Q． General linear chirplet transform． Mech Syst Signal Process，2016，70: 958 ［11］ Cheng J S，Yang Y，Yu D J． The envelope order spectrum based on generalized demodulation time--frequency analysis and its ap￾plication to gear fault diagnosis． Mech Syst Signal Process，2010， 24( 2) : 508 ［12］ Li C，Liu Z X，Zhou F X，et al． Application of generalized de￾modulation in bearing fault diagnosis of inverter fed induction mo￾tors / / Proceeding of the 11th World Congress on Intelligent Con￾trol and Automation IEEE． Shenyang，2014: 2328 ［13］ Wang Y，Xu G H，Luo A L，et al． An online tacholess order tracking technique based on generalized demodulation for rolling bearing fault detection． J Sound Vib，2016，367: 233 ［14］ Olhede S，Walden A T． A generalized demodulation approach to time-- frequency projections for multicomponent signals． Proc Math Phys Eng Sci，2005，461( 2059) : 2159 ［15］ Cheng J S，Yang Y，Yu D J． Application of the improved gener￾alized demodulation time--frequency analysis method to multi￾component signal decomposition． Signal Process，2009，89( 6) : 1205 · 016 ·