·1334 工程科学学报，第38卷，第9期 (b) 0.5 (a) 0.5 0.2 0 0 -02 0.5 2 D 时间/s -0.5 02 2.117 7753 294 2.230 02 0.2 0 0 2.0 2.1 2.22.3 2.4 2.5 2.6 -0.1 时间/s 时间/s 0.03 2.118 2.392 0.02 0.02 2.095 2.255 2.369 2.232 0.0 菱01 2.0 2.1 2.2 2.3 2.4 2.5 2.6 时间s 时间/s 1.5 0.015 ) 人12f f+1.2 2f-126 2f+1,2f 1.0 0.010 2f 0.005 00 60 80 100 20 40 60 80 100 频率Hz 频率Hz 图5内图故障信号分析结果.(a)时域波形：(b)第1~6个本质模式函数：(c)山1时域局部波形：(d)u,瞬时能量波形：(e)山1瞬时能量局 部波形：(0山1瞬时能量频谱：(g包络谱 Fig.5 Analysis results of the inner race fault signal:(a)time domain waveform:(b)intrinsic mode functions16:(c)u time domain local wave- form:(d)u instantaneous energy waveform:(e)u instantaneous energy local waveform:(f)u instantaneous energy spectrum:(g)envelope spec- trum [11]Dragomiretskiy K,Zosso D.Variational mode decomposition [15]Wang Y,Markert R,Xiang J,et al.Research on variational IEEE Trans Signal Process,2014,62(3):531 mode decomposition and its application in detecting rub-impact [12]Huang N E,Shen Z,Long S R.A new view of nonlinear water fault of the rotor system.Mech Syst Signal Process,2015,60: waves:the Hilbert spectrum.Annu Rev Fluid Mech,1999,31 243 (1):417 [16]Zhao X N,Feng Z P.Fault diagnosis of rolling element bearing [13]Wu Z H,Huang N E.Ensemble empirical mode decomposition: based on ensemble empirical mode decomposition and cross ener- a noise assisted data analysis method.Adr Adapt Data Anal, gy operator.Chin J Eng,2015,37(Suppl 1):65 2009,1(1):1 (赵晓宁，冯志鹏.基于集合经验模式分解和交叉能量算子 [14]Rilling G,Flandrin P.On the influence of sampling on the em- 的滚动轴承故障诊断.工程科学学报，2015,37（增刊1）： pirical mode decomposition /Proceedings of IEEE Conference on 65) Acoustics,Speech and Signal Processing.Toulouse,2006:II-44工程科学学报，第 38 卷，第 9 期 图 5 内圈故障信号分析结果． ( a) 时域波形; ( b) 第 1 ～ 6 个本质模式函数; ( c) u1 时域局部波形; ( d) u1 瞬时能量波形; ( e) u1 瞬时能量局 部波形; ( f) u1 瞬时能量频谱; ( g) 包络谱 Fig． 5 Analysis results of the inner race fault signal: ( a) time domain waveform; ( b) intrinsic mode functions 1--6; ( c) u1 time domain local wave￾form; ( d) u1 instantaneous energy waveform; ( e) u1 instantaneous energy local waveform; ( f) u1 instantaneous energy spectrum; ( g) envelope spec￾trum ［11］ Dragomiretskiy K，Zosso D． Variational mode decomposition． IEEE Trans Signal Process，2014，62( 3) : 531 ［12］ Huang N E，Shen Z，Long S Ｒ． A new view of nonlinear water waves: the Hilbert spectrum． Annu Ｒev Fluid Mech，1999，31 ( 1) : 417 ［13］ Wu Z H，Huang N E． Ensemble empirical mode decomposition: a noise assisted data analysis method． Adv Adapt Data Anal， 2009，1( 1) : 1 ［14］ Ｒilling G，Flandrin P． On the influence of sampling on the em￾pirical mode decomposition / / Proceedings of IEEE Conference on Acoustics，Speech and Signal Processing． Toulouse，2006: III-44 ［15］ Wang Y，Markert Ｒ，Xiang J，et al． Ｒesearch on variational mode decomposition and its application in detecting rub-impact fault of the rotor system． Mech Syst Signal Process，2015，60: 243 ［16］ Zhao X N，Feng Z P． Fault diagnosis of rolling element bearing based on ensemble empirical mode decomposition and cross ener￾gy operator． Chin J Eng，2015，37( Suppl 1) : 65 ( 赵晓宁，冯志鹏． 基于集合经验模式分解和交叉能量算子 的滚动轴承故障诊断． 工程科学学报，2015，37 ( 增刊 1) : 65) ·1334·