機械的狀態監控對於產業日漸重要，因為產業需要提高機械的可靠性，並且減少機械故障可能造成的經濟損失，以提升產業競爭力。在監測旋轉機械狀態的領域中，使用振動訊號進行分析是相當普遍的。透過比較機械運行時，正常與故障情況下產生的訊號，將可能檢測出軸承缺陷錯誤的類型。一般情況下，軸承錯誤診斷流程可以分為三個主要步驟：特徵擷取、特徵選取與錯誤情況的分類。在本論文中，我們提出了一個錯誤檢測的演算法，以區分不同種類的軸承故障。首先，收集振動訊號，並使用不同方法擷取其特徵，如多尺度熵(Multiscale Entropy, MSE)和多尺度方均根(Multiscale Root Mean Square, MSRMS)演算法。其次，使用費雪法(Fisher Score, FS)選取最佳的特徵。最後，使用最佳的特徵與倒傳遞網路 (Backpropagation Neural Network, BPN)來建立錯誤狀態分類的模型。在我們的模擬中，使用了凱斯西儲大學(CWRU)的軸承振動訊號資料。實驗結果表明，此錯誤診斷的流程應用於軸承訊號具有相當高的辨識率。

Machine condition monitoring is gaining importance in industry because of the need to increase reliability and to decrease the possibility of production loss due to machine breakdown. The use of vibration signals is quite common in the field of condition monitoring of rotating machinery. By comparing the signals of a machine running in normal and faulty conditions, detection of fault types of bearing defects is possible. Generally, a bearing fault diagnosis process can be decomposed into three major steps: feature extraction, feature selection and fault condition classification. In this dissertation, we propose a fault detection algorithm to distinguish different types of bearing fault. Firstly, the features of vibration signals collected from different conditions were extracted by multiscale entropy (MSE) and multiscale root mean square (MSRMS) algorithm. Secondly, the optimal feature set is selected by Fisher score. Thirdly, the optimal feature set and backpropagation neural network (BPN) was used to build the model of fault classifier. In our simulations, the vibration signal datasets of bearing from Case Western Reserve University (CWRU) are utilized. Experimental results demonstrate that the proposed algorithm provides a high accuracy of prediction on the test data.

黃建中， 「2011年工具機產銷年度統計」， 台灣區工具機暨零組件工業同業公會網站， http://www.tmba.org.tw/type3_show_detail.asp?1125,
24,5,1。
朱鳳傳、康鳳梅、黃泰翔、施議訓、劉紀嘉、許榮添、簡慶郎、詹世良， 機械設計製造手冊，全華科技圖書股份有限公司，2003。
“ISO 10816,” 1995.
“ISO 2372,” 1974.
R. Barron, “Engineering Condition Monitoring: Practice, Methods and Applications,” University of Strathcycle, Glasgow, Longman, 1996.
R.B.W. Heng and M.J.M. Nor, "Statistical analysis of sound and vibration signals for monitoring rolling element bearing condition," Applied Acoutics, vol. 53, no. 1-3, pp. 211-226, 1998.
H. Ahmadi and K. Mollazade, "Bearing Fault Diagnosis of a Mine Stone Crasher by Vibration Condition Monitoring Technique," Research Journal of Applied Sciences, Engineering and Technology, vol. 1, no. 3, pp. 112-115, 2009.
B. Sreejith, A. K. Verma and A. Srividya, "Fault Diagnosis of Rolling Element Bearing Using Tme-Domain Features and Neural Networks," IEEE Proceedings of ICIIS, pp. 1-6, 2008.
M. Costa, A. L. Goldberger and C. K. Peng, "Multiscale Entropy Analysis of Complex Physiologic Time Series," Physical Review Letters, vol. 89, no. 6, pp. 068102-1 - 068102-4, 2002.
L. Zhang, G. Xiong, H. Liu, H. Zou and W. Guo, "An Intelligent Fault Diagnosis Method Based on Multiscale Entropy and SVMs," Springer-Verlag Berlin Heidelberg, pp. 724-732, 2009.
J. L. Lin, J. Y. C. Liu, C. W. Li, L. F. Tsai and H. Y. Chung, "Motor Shaft Misalignment Detection Using Multiscale Entropy with Wavelet Denoising," Expert Systems with Applications, vol. 37, pp. 7200-7204, 2010.
吳求文、王俊傑、吳順德，「基於多尺度熵、區別指標與支持向量機之旋轉機械異常診斷系統」，第二十八屆中國機械工程全國學術研討會，台中市，2011。
G. L. Xiong, L. Zhang, H. S. Liu, H. J. Zou and W. Z. Guo, "A Comparative Study on ApEn, SampEn and Their Fuzzy Counterparts in a Multiscale Framework for Feature Extraction," Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), vol. 11, no. 4, pp. 270-279, 2010.
J. Weston, S. Mukherjee, O. Chapelle, M. Pontil, T. Poggio and V. Vapnik, "Feature Selection for SVMs," Advances in Neural Information Processing Systems, 2000.
W. C. Kao, M. C. Hsu and Y. Y. Yang, "Local Contrast Enhancement and Adaptive Feature Extraction for Illumination-Invariant Face Recognition," Pattern Recognition, vol. 43, no. 5, pp. 1736-1747, May 2010.
H. Wang and P. Chen, "Intelligent Diagnosis Method for Rolling Element Bearing Faults Using Possibility Theory and Neural Network," Computers & Industrial Engineering, vol. 60, no. 4, pp. 511-518, May 2011.
H. Wang and P. Chen, "Fuzzy Diagnosis Method for Rotating Machinery in Variable Rotating Speed," IEEE Sensors Journal, vol. 11, no. 1, pp. 23-34, Jan. 2011.
B. Li, M. Y. Chow, Y. Tipsuwan and J. C. Hung, "Neural-Network-based Motor Rolling Bearing Fault Diagnosis," IEEE Transactions on Industrial Electronics, vol. 47, pp. 1060-1069, Oct. 2000.
N. Gebraeel, M. Lawley, R. Liu and V. Parmeshwaran, "Residual Life Predictions from Vibration-Based Degradation Signals: A Neural Network Approach," IEEE Transactions on Industrial Electronics, vol. 51, no. 3, pp. 694-700, 2004.
I. M. Lee and J. H. Lee, "Prediction of Pile Bearing Capacity Using Artificial Neural Networks," Computers and Geotechnics, vol. 18, no. 3, pp. 189-200, 1996.
N. S. Vyas and D. Satishkumar, "Artificial Neural Network Design for Fault Identification in a Rotor-Bearing System," Mechanism and Machine Theory, vol. 36, no. 2, Feb. 2001.
J. Rafiee, F. Arvani, A. Harifi and M. H. Sadeghi, "Intelligent Condition Monitoring of a Gearbox Using Artificial Neural Network," Mechanical Systems and Signal Processing, vol. 21, no. 4, pp. 1746-1754, May 2007.
C. C. Wang, Y. Kang, P. C. Shen, Y. P. Chang and Y. L. Chung, "Applications of Fault Diagnosis in Rotating Machinery by Using Time Series Analysis with Neural Network," Expert Systems with Applications, vol. 37, no. 2, pp. 1696-1702, 2010.
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, no. 5, pp. 8862-8875, July 2009.
M. Costa, A. L. Goldberger and C. K. Peng, "Multiscale Entropy Analysis of Biological Signals," Physical Review E, vol. 71, pp. 021906-1-021906-18, 2005.
J. S. Richman and J. R. Moorman, "Physiological Time-Series Analysis Using Approximate Entropy and Sample Entropy," Am J Physiol Heart Circ Physiol, vol. 278, no. 6, pp. H2039-H2049, 2000.
吳萬益，企業研究方法，華泰文化事業股份有限公司，2005。
W. W. Cooley and P. R. Lohnes, Multivariate data analysis, New York, 1971.
葉怡成，類神經網路模式應用與實作第七版，儒林出版社，2000。
羅華強，類神經網路-MATLAB的應用，清蔚科技，2001。
D. E. Rumelhart, G. E. Hinton and R. J. Williams, "Learning Internal Representation by Error Propagation," in Parallel Distributed Processing, D. E. Rumelhart and McClelland(Eds), MIT, Press, Cambridge, MA, vol. 1, pp. 318-362, 1986.
S. Haykin, Neural Networks : A Comprehensive Foundation, Prentice Hall International Editions, 1999.
趙景明、梁淑芳，「導入LM法之平行倒傳遞演算法」，資訊管理展望，第8卷，第2期，第85~108頁，2006年12月。
M.I.A Lourakis, "A Brief Description of the Levenberg–Marquardt Algorithm Implemented by Levmar," February 2005. [Online]. Available: www.ics.forth.gr/~lourakis/levmar/levmar.pdf.
M. T. Hagan and M. B. Menhaj, "Training Feedforward Networks with the Marquardt Algorithm," IEEE Trans. Neural Networks, vol. 5, pp. 989-993, 1994.
M. F. Moller, "A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning," Neural Networks, vol. 6, no. 4, pp. 525-533, 1993.
H. Demuth and M. Beale, Neural network toolbox user's guide, version 4, Natick, MA: The MathWorks Inc., 2003.
Case Western Reserve University Bearing Data Center Website, http://www.eecs.case.edu/laboratory/bearing/welcome_overview.htm.