本研究利用希爾伯特-黃轉換針對旋轉機械的軸承元件於變轉速下，軸承發生外圈損壞、內圈損壞、滾子損壞和複合故障等情形進行故障診斷。首先，利用階次追蹤方法將轉速變動因子抽離，使非穩態的訊號轉換成穩態的角度域訊號，再提取角度域訊號之包絡線透過希爾伯特-黃轉換進行分析，於分解出來的固有模態函數和希爾伯特邊際譜探討軸承不同的損壞特徵，並經由振幅正規化後使得故障特徵不會隨著變轉速影響，最後，以支持向量機進行單一故障軸承的故障診斷，且利用此分類器對複合故障軸承進行故障診斷。

In this study, Hilbert-Huang transform (HHT) is utilized for diagnosing the roller bearing faults, such as outer race defect, inner race defect, roller defect and multi-fault, under variable rotation speed. The vibration signals are first measure through the order tracking technique, so that the vibration signals are detected with identical angle increment and thus the vibration signals are stationary without the factor of variable shaft rotation speed. The envelope signals of the measurements are analyzed by Hilbert-Huang transform approach. The features of the faulted bearings are extracted by investigating the intrinsic mode functions (IMFs) as well as the marginal Hilbert spectra. The extracted features of the faulted bearing are then re-scaled through the amplitude normalization, so that the vibration energy are not affected by the variable rotation speed. Finally, the support vector machine is employed to identify the individual defect of bearing. The same SVM structure is also used to diagnose the occurrence of multi-fault in bearings.

[1] N. E. Huang, Z. Shen, S. R. Long, M. L. C. Wu, H. H. Shih, Q. N. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, vol. 454, pp. 903-995, 1998.
[2] Z. H. Wu and N. E. Huang, “A study of the characteristics of white noise using the empirical mode decomposition method,” Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, vol. 460, pp. 1597-1611, 2004.
[3] Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Center for Ocean-Land-Atmosphere Studies, Technical Report series, vol. 193, 2005.
[4] Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Advances in Adaptive Data Analysis, vol. 1, pp. 1-41, 2009.
[5] R. B. Randall and J. Antoni, “Rolling element bearing diagnostics-A tutorial,” Mechanical Systems and Signal Processing, vol. 25, pp. 485-520, 2011.
[6] B. Samantha and K.R. Al.-Balushi, “Artificial Neural Networks based fault diagnostics of rolling element bearings using time domain features,” Mechanical Systems and Signal Processing, vol. 17, pp. 317–328, 2003.
 
[7] P.K. Kankar, Satish C. Sharma and S.P. Harsha, “Fault diagnosis of ball bearings using machine learning methods,” Expert Systems with Applications, vol. 38, pp. 1876–1886, 2011.
[8] S. A. McInerny and Y. Dai, “Basic Vibration signal processing for bearing fault detection,” IEEE Transactions on Education, vol. 46, pp. 149–156, 2003.
[9] N. Tandon and A. Choudhury, “An analytical model for the prediction of the vibration response of rolling element bearings due to a localized defect,” Journal of Sound and Vibration, vol. 205 (3), pp. 275–292, 1997.
[10] D. Ho and R.B. Randall, “Optimization of bearing diagnostic techniques using simulated and actual bearing fault signals,” Mechanical Systems and Signal Processing, vol. 14, pp. 763–788, 2000.
[11] R.B. Randall, J. Amtoni and S. Chobsaard, “The relationship between spectral correlation and envelope analysis in the diagnostics of bearing faults and other cyclostationary machine signals,” Mechanical Systems and Signal Processing, vol. 15, pp.945–962, 2001.
[12] V. Purushotham, S. Narayanana and A.N. Prasad Suryanarayana, “Multi-fault diagnosis of rolling bearing elements using wavelet analysis and hidden Markov model based fault recognition,” NDT and E International, vol. 38, pp. 654–664, 2005.
[13] S. Prabhakar, A.R. Mohanty and A.S. Sekhar, “Application of discrete wavelet transform for detection of ball bearing race faults,” Tribology International, vol. 35, pp. 793–800, 2002.
 
[14] D. Yu, J. Cheng and Y. Yang, “Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings,” Mechanical Systems and Signal Processing, vol. 19, pp. 259–270, 2005.
[15] T.Y. Wu and Y.L. Chung, “Misalignment diagnosis of rotating machinery through vibration analysis via hybrid EEMD and EMD approach,” Smart Materials and Structures, vol. 18, 095004, 2009.
[16] T.Y. Wu, Y.L. Chung and C.H. Liu, “Looseness diagnosis of rotating machinery via vibration analysis through Hilbert-Huang transform approach,” Journal of Vibration and Acoustics-Transactions of the ASME, vol. 132, 031005, 2010.
[17] T.Y. Wu, J.C. Chen and C.C. Wang, “Characterization of gear faults in variable rotating speed using Hilbert-Huang transform and instantaneous dimensionless frequency normalization,” Mechanical Systems and Signal Processing, vol. 30, pp. 103–122, 2012.
[18] R. Yan and R. X. Gao, “Hilbert–Huang transform-based vibration signal analysis for machine health monitoring,” IEEE Transactions on Instrumentation and Measurement, vol. 55, pp. 2320-2328, 2006.
[19] R. Potter and M. Gribler, “Computed order tracking obsoletes older methods,” SAE Technical Paper 891131, 1989.
[20] K. R. Fyfe and E. D. S. Munck, “Analysis of computed order tracking,” Mechanical Systems and Signal Processing, vol. 11, pp. 187-205, 1997.
[21] H. Vold and J. Leuridan, “High resolution order tracking and extreme slew rates, using Kalman tracking filters,” SAE Paper 931288, 1993.
 
[22] M.R. Bai, J. Huang, M. Hong and F. Su, “Fault diagnosis of rotating machinery using an intelligent order tracking system,” Journal of Sound and Vibration, vol.280, pp. 699–718, 2005.
[23] J. D. Wu, Y. H. Wang and M. R. Bai, “Development of an expert system for fault diagnosis in scooter engine platform using fuzzy-logic inference,” Expert Systems with Applications , vol. 33(4), pp. 1063-1075, 2007.
[24] J. D. Wu, Y. H. Wang, P. H. Chiang and M. R. Bai, “A study of fault diagnosis in a scooter using adaptive order tracking technique and neural network,” Expert Systems with Applications, vol. 36(1), pp. 49-56, 2009.
[25] J.D. Wu and J.J. Chan, “Faulted gear identification of a rotating machinery based on wavelet transform and artificial neural network,” Expert Systems with Applications, vol. 36, pp. 8862–8875, 2009.
[26] N. Saravanan and K.I. Ramachandran, “Fault diagnosis of spur bevel gear box using discrete wavelet features and decision tree classification,” Expert Systems with Applications, vol. 36, pp. 9564–9573, 2009.
[27] Y. Yang, D. J. Yu, and J. S. Cheng, “A fault diagnosis approach for roller bearing based on IMF envelope spectrum and SVM,” Measurement, vol. 40, pp. 943-950, 2007.
[28] P. D. McFadden and J. D. Smith, “The vibration produced by multiple point defects in a rolling element bearing,” Journal of Sound and Vibration, vol. 98(2), pp. 263-273, 1985.
 
[29] M. C. Pan and W. C. Tsao, “Using appropriate IMFs for envelope analysis in multiple fault diagnosis of ball bearings,” International Journal of Mechanical Sciences, vol. 69, pp. 114-124, 2013.
[30] J. I. Taylor, The Vibration Analysis Handbook: A Practical Guide for Solving Rotating Machinery Problems (2nd ed), United Kingdom: Vibration Consultants, 2003.
[31] C. Cortes and V. Vapnik, “Support-vector networks,” Machine Learning, vol. 20, pp. 273-297, 1995.
[32] C. W. Hsu and C. J. Lin, “A comparison of methods for multiclass support vector machines,” IEEE Transactions on Neural Networks, vol. 13(2), pp. 415-423, 2002.
[33] C. C. Chang and C. J. Lin, LIBSVM -- A Library for Support Vector Machines, Available: http://www.csie.ntu.edu.tw/~cjlin/libsvm/.
[34] 賴家祥, 運用希爾伯特-黃轉換及無因次單位瞬時頻率正規化技術之特徵擷取於非固定轉速之軸承故障診斷, 桃園縣, 國立中央大學機械工程研究所碩士論文, 2012。