张景玲等：基于周期势系统随机共振的轴承故障诊断 .995· 势系统随机共振方程(3)中six展开成麦克劳林级 tials.J Stat Phys,1993,70(1-2):501 数后含有无穷多项，这就相当于优化了无穷多个参 [6]Saikia S,Jayannavar A M,Mahato MC.Stochastic resonance in 数，因此所得效果也较好.综上所述，在达到最优输 periodic potentials.Phys Rer E,2011,83(6):061121-1 [7]Saikia S.The role of damping on stochastic rsonance in a periodic 出时，周期势系统自适应随机共振在减少干扰频率 potential.Physica A,2014,416:411 成分、减少迭代次数、缩短计算时间以及提高改进的 [8]Xie Y H,Liu X L,Liu H G,et al.Improved frequency-shifted 信噪比方面都比双稳态系统自适应随机共振更有 and re-scaling stochastic resonance for gear fault diagnosis.Trans 优势 Chin Soc Agrie Eng,2016,32(8):70 (谢有浩，刘晓乐，刘后广，等.基于改进移颜变尺度随机共 3结论 振的齿轮故障诊断.农业工程学报，2016,32(8)：70) [9]Leng Y G.Wang T Y,Qin X D,et al.Power spectrum research 本文使用普通变尺度方法，并结合周期势系统 of twice sampling stochastic resonance response in a bistable sys- 自适应随机共振理论实现了强噪声背景下轴承滚动 tem.Acta Phys Sin,2004,53(3):717 体的故障诊断.主要得出了以下结论： (冷永刚，王太勇，秦旭达，等.二次采样随机共振频谱研究 (1)将普通变尺度方法和自适应随机共振相结 与应用初探.物理学报，2004,53(3)：717) 合能够有效地提取轴承滚动体在强噪声背景下的微 [10]Dai DY.He Q B.Multiscale noise tuning stochastic resonance 弱故障特征信息 enhances weak signal detection in a circuitry system.Meas Sci Technol,2012,23(11):115001-1 (2)周期势系统自适应随机共振与双稳态系统 [11]He Q B.Wang J.Effects of multiscale noise tuning on stochastic 自适应随机共振相比，干扰频率成分少，信噪比的值 resonance for weak signal detection.Digit Signal Process,2012 有所提高，而且所用时间短、迭代次数少 22(4):614 (3)实验信号验证表明基于普通变尺度和周期 [12]Zhang X F,Hu N Q,Hu L,et al.Enhanced detection of bear- 势系统自适应随机共振的轴承滚动体故障诊断具有 ing faults based on signal cepstrum pre-whitening and stochastic resonance.J Mech Eng,2012,48(23):83 可行性 (张晓飞，胡茑庆，胡雷，等.基于倒谱预白化和随机共振的 轴承故障增强检测.机械工程学报，2012,48(23)：83) 参考文献 [13]Gammaitoni L,Hanggi P,Jung P,et al.Stochastic resonance. [1]Li Z N,Zhu M,Chu F L,et al.Mechanical fault diagnosis meth- Rer Mod Phys,1998,70(1):223 od based on empirical wavelet transform.Chin J Sci Instrum, [14]Lu S L,He Q B,Zhang H B,et al.Enhanced rotating machine 2014.35(11):2423 fault diagnosis based on time-delayed feedback stochastic reso- (李志农，朱明，褚福磊，等.基于经验小波变换的机械故障 nance.J Vib Acoustics,2015,137(5):051008 诊断方法研究.仪器仪表学报，2014,35(11)：2423) [15]Gauthier P A,Gerard A,Camier C,et al.Acoustical inverse [2]Lei Y G.Lin J,He Z J.et al.A review on empirical mode de- problems regularization:direct definition of filter factors using composition in fault diagnosis of rotating machinery.Mech Syst signal-to-noise ratio.J Sound Vib,2014,333(3):761 Signal Process,2013,35(1-2)108 [16]Chen X H,Cheng G,Shan X L,et al.Research of weak fault [3]Benzi R,Sutera A,Vulpiana A.The mechanism of stochastic res feature information extraction of planetary gear based on ensemble onance.J Phys A Math Gen,1981,14:1453 empirical mode decomposition and adaptive stochastic resonance. [4]Lei Y G,Han D,Lin J,et al.New adaptive stochastic resonance Mes,2015,73:55 method and its application to fault diagnosis.I Mech Eng,2012, [17]Marini F,Walezak B.Particle swarm optimization PSO)-a tu- 48(7):62 torial.Chemom Intell Lab Syst,2015,149:153 (雷亚国，韩冬，林京，等.自适应随机共振新方法及其在故 [18]Guedria N B.Improved accelerated PSO algorithm for mechanical 障诊断中的应用.机械工程学报，2012,48(7)：62) engineering optimization problems.Appl Soft Comput,2016,40: [5]Fronzoni L,Mannella R.Stochastic resonance in periodic poten- 455张景玲等: 基于周期势系统随机共振的轴承故障诊断 势系统随机共振方程(3)中 sinx 展开成麦克劳林级 数后含有无穷多项,这就相当于优化了无穷多个参 数,因此所得效果也较好. 综上所述,在达到最优输 出时,周期势系统自适应随机共振在减少干扰频率 成分、减少迭代次数、缩短计算时间以及提高改进的 信噪比方面都比双稳态系统自适应随机共振更有 优势. 3 结论 本文使用普通变尺度方法,并结合周期势系统 自适应随机共振理论实现了强噪声背景下轴承滚动 体的故障诊断. 主要得出了以下结论: (1)将普通变尺度方法和自适应随机共振相结 合能够有效地提取轴承滚动体在强噪声背景下的微 弱故障特征信息. (2)周期势系统自适应随机共振与双稳态系统 自适应随机共振相比,干扰频率成分少,信噪比的值 有所提高,而且所用时间短、迭代次数少. (3)实验信号验证表明基于普通变尺度和周期 势系统自适应随机共振的轴承滚动体故障诊断具有 可行性. 参 考 文 献 [1] Li Z N, Zhu M, Chu F L, et al. Mechanical fault diagnosis meth鄄 od based on empirical wavelet transform. Chin J Sci Instrum, 2014, 35(11): 2423 (李志农, 朱明, 褚福磊, 等. 基于经验小波变换的机械故障 诊断方法研究. 仪器仪表学报, 2014, 35(11): 2423) [2] Lei Y G, Lin J, He Z J, et al. A review on empirical mode de鄄 composition in fault diagnosis of rotating machinery. Mech Syst Signal Process, 2013, 35(1鄄2): 108 [3] Benzi R, Sutera A, Vulpiana A. The mechanism of stochastic res鄄 onance. J Phys A Math Gen, 1981, 14: L453 [4] Lei Y G, Han D, Lin J, et al. New adaptive stochastic resonance method and its application to fault diagnosis. J Mech Eng, 2012, 48(7): 62 (雷亚国, 韩冬, 林京, 等. 自适应随机共振新方法及其在故 障诊断中的应用. 机械工程学报, 2012, 48(7): 62) [5] Fronzoni L, Mannella R. Stochastic resonance in periodic poten鄄 tials. J Stat Phys, 1993, 70(1鄄2): 501 [6] Saikia S, Jayannavar A M, Mahato M C. Stochastic resonance in periodic potentials. Phys Rev E, 2011, 83(6): 061121鄄1 [7] Saikia S. The role of damping on stochastic rsonance in a periodic potential. Physica A, 2014, 416: 411 [8] Xie Y H, Liu X L, Liu H G, et al. Improved frequency鄄shifted and re鄄scaling stochastic resonance for gear fault diagnosis. Trans Chin Soc Agric Eng, 2016, 32(8): 70 (谢有浩, 刘晓乐, 刘后广, 等. 基于改进移频变尺度随机共 振的齿轮故障诊断. 农业工程学报, 2016, 32(8): 70) [9] Leng Y G, Wang T Y, Qin X D, et al. Power spectrum research of twice sampling stochastic resonance response in a bistable sys鄄 tem. Acta Phys Sin, 2004, 53(3): 717 (冷永刚, 王太勇, 秦旭达, 等. 二次采样随机共振频谱研究 与应用初探. 物理学报, 2004, 53(3): 717) [10] Dai D Y, He Q B. Multiscale noise tuning stochastic resonance enhances weak signal detection in a circuitry system. Meas Sci Technol, 2012, 23(11): 115001鄄1 [11] He Q B, Wang J. Effects of multiscale noise tuning on stochastic resonance for weak signal detection. Digit Signal Process, 2012, 22(4): 614 [12] Zhang X F, Hu N Q, Hu L, et al. Enhanced detection of bear鄄 ing faults based on signal cepstrum pre鄄whitening and stochastic resonance. J Mech Eng, 2012, 48(23): 83 (张晓飞, 胡茑庆, 胡雷, 等. 基于倒谱预白化和随机共振的 轴承故障增强检测. 机械工程学报, 2012, 48(23): 83) [13] Gammaitoni L, Hanggi P, Jung P, et al. Stochastic resonance. Rev Mod Phys, 1998, 70(1): 223 [14] Lu S L, He Q B, Zhang H B, et al. Enhanced rotating machine fault diagnosis based on time鄄delayed feedback stochastic reso鄄 nance. J Vib Acoustics, 2015, 137(5): 051008 [15] Gauthier P A, G佴rard A, Camier C, et al. Acoustical inverse problems regularization: direct definition of filter factors using signal鄄to鄄noise ratio. J Sound Vib, 2014, 333(3): 761 [16] Chen X H, Cheng G, Shan X L, et al. Research of weak fault feature information extraction of planetary gear based on ensemble empirical mode decomposition and adaptive stochastic resonance. Meas, 2015, 73: 55 [17] Marini F, Walczak B. Particle swarm optimization (PSO)—a tu鄄 torial. Chemom Intell Lab Syst, 2015, 149: 153 [18] Guedria N B. Improved accelerated PSO algorithm for mechanical engineering optimization problems. Appl Soft Comput, 2016, 40: 455 ·995·