在這數位科技發達的年代，拜電腦運算速度大幅提升之賜，許多在過去需要經過大量運算的分析，如今均可在短時間內獲得快速解答。因此，類神經網路應運而生，在學術界各領域之應用如雨後春筍般迅速成為熱門焦點，其原因便是能快速處理大量複雜的樣本資訊，建立網路輸入-輸出間的非線性對應關係，並不斷進行學習與修正，直到獲得最佳的解為止。
過去的研究顯示，利用離散小波轉換分析可以偵測到受損平板損傷的位置，但無法得知其損傷的深度與長度。本文旨在結合類神經網路與二維離散小波轉換應用於偵測平板裂縫破損程度上。在數值分析中，本研究利用平板破損程度不同時，其模態振型也會隨之產生微小改變的特性，經過二維離散小波轉換分析後並擷取其類神經網路的訓練樣本，藉此架構一套可以判別平板裂縫破損程度的偵測系統。此外，本研究並以實際實驗量測來驗證模擬類神經網路破損程度識別系統的可靠性，使本研究更具有實用價值。

In this digital generation, in order to analyze a large amount of data during a short period of time, researchers have devised various kinds of tools and methods to increase and maximize the speed of calculation. Neural networks are one of the many popular examples for this purpose. They are used in many research fields and industries as neural networks can process a lot of complex information efficiently and quickly. Another function of neural networks is to establish the correspondence between nonlinear input-output relationships and compute optimal solutions from learning and revision.
Previous studies have demonstrated that the discrete wavelet transform technique can be used to detect crack locations of a damaged plate. However, this method is unable to identify the depth and length of the damaged plates. In the thesis, the study focuses on the ability to detect plates with multiple cracks. The core concept is about the combination of artificial neural networks with two-dimensional discrete wavelet transform to form a system which is able to identify effectively the length and depth of damage in the cracks of plates. In numerical analysis, the mode shapes vary due to the difference in the degree of damage of the plates. The collected data is analyzed through the use of two-dimensional discrete wavelet and the trial samples of neural networks. Lastly, the investigation verifies the reliability of neural networks through practical measurements and experimental results which further proves the credibility of using this method for analyzing data.

[1] Cawley, P., and Adams, R.D., “The Location of Defects in Structures from Measurement of Natural Frequencies,” Journal of Strain Analysis, 14, 1979.
[2] Choubey, A., Sehgal, D.K. and Tandon, N., “Finite Clement Analysis of Vessels to Study Changes in Natural Frequencies due to Cracks,” International Journal of Pressure Vessels and Piping, Vol. 83, Issue.3, pp.181-187, 2006.
[3] Chen, Wenyuan, Lei Zhao and Guotang Bi, “Application of Neural Network and Wavelet Analysis in Monitoring Multiple Structural Damage,” International Conference on Electronic Measurement and Instruments, pp.4463-4467, 2007.
[4] Rumelhart, E. David, McClelland, L. James, and the PDP Research Group, “Parallel Distributed Processing: xplorations in the Microstructure of Cognition,” Cambridge, Mass, 1986.
[5] Daubechies, I., “Ten Lectures on Wavelets,” SIAM, Philadelphia, 1992.
[6] Deng, X., Wang, Q., “Crack Detection Using Spatial Measurements and Wavelet,” International Journal of Fracture, Vol. 91, 1998.
[7] Diao, Yan-Song, Hua-Jun Li and Yan Wang, “A Two-Step Structural Damage Detection Approach Based on Wavelet Packet Analysis and Neural Network,” Proceedings of the 2006 International Conference on Machine Learning and Cybernetics, pp.3128-3133, 2006.
[8] Fuchs, H.O., “Metal Fatigue in Engineering,” John-Wiley & Sons Inc, 1980.
[9] Hopfield, J., “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proceedings of the National Academy of Sciences, vol.79, No.8, pp.2554-2558, 1982.
[10]Hopfield, J., “Neurons with Graded Response Have Collective Computational Properties Like Those of Two-state Neurons,” Proceedings of the National Academy of Sciences, Vol.81, No.10, pp. 3088-3092, 1984.
[11]Kudva, J. N., Munir, N. and Tan, P. W., “Damage Detection in Smart Structures Using Neural Networks and Finite-Element Analyses,” Smart Materials and Structures, Vol.1, No.2, pp. 108-112, 1992.
[12]Liew, K. M., Wang, Q., “Application of Wavelet Theory for Crack Identication in Structures”, Journal of engineering Mechanics, 149 Vol.124(2), pp.152-157, 1998.
[13]Loutridis, S., Douka, E., and Trochidis, A., “Crack Identification in Beams Using Wavelet Analysis,” International Journal of Solids and Structures , Vol.40, pp.3557-3569, 2003.
[14]Morlet, J., Arens, G., Fourgeau, I., and Giard, D., “Wave Propagation and Sampling Theory”, Geophysics, 47, pp.203-236, 1982.
[15]Morlet, J., “Sampling Theory and Wave Propagation”, NATO ASI Series, Issues in Acoustic Signal/Image Processing and Recognition , Vol. I, pp.233-261, 1983.
[16]Meyer, Y., Ondettes et Functions Splines, Lectures given at the University of Torino, Italy, 1986.
[17]Meyer, Y., Ondettes, Functions Splines et Analyses Graduees, Seminaire EDP, Ecole Polytechnique, Paris, France, 1986.
[18]Mallat, S.G., “A Theory for Multiresolution Signal Decomposition, The Wave Representation,” Comm. Pure Appl. Math, 41, pp.674-693, 1988.
[19]Meyer, Y., “Wavelets Algorithms and Application,” Siam, 1993.
[20]Messina, A., Jones, I.A., “Damage Detection and Localization Using Natural Frequency Change,” 14th International Modal Analysis Conference, Orlando, pp.67-76, 1996.
[21]Mallat, S., “A Wavelet Tour of Signal Processing,” Academic Press, USA, 1998.
[22]Messina, A., Williams, E.J., Contursi, T., “Structural Damage Detection by Sensitivity and Statistical-Based Method,” Journal of Sound and Vibration, 216, pp.791-808, 1998.
[23]Narkis, Y., “Identification of Crack Location in Vibrating Simply Supported Beams,” Journal of Sound and Vibration, 172, pp.549-558, 1994.
[24]Pandey, A.K., Biswas, M., Samman, M.M., “Damage Detection from Changes in Curvature Mode Shapes,” Journal of Sound and Vibration, pp. 321-332, 1991.
[25]Ratcliffe, C.P., “Damage Detection Using a Modified Laplacian Operator on Mode Shape Data,” Journal of Sound and Vibration, 204,pp.505-517, 1997.
[26]Surace, C., and Ruotolou, R., “Crack Detection of a Beam Using the Wavelet Transform,” Proceedings of the 12th International Modal Analysis Conference, Honolulu, pp.1141-1147, 1994.
[27]Stubbs, N., Kim, J.T., “Damage Localization in Structures Without Baseline Modal Parameters,” American Institute of Aeronautics and Astronautics Journal, 34, pp. 1644-1649, 1996.
[28]Sampaio, R.P.C., Maia, N.M.M., Silva, J.M.M., “Damage Detection Using the Frequency-Response-Function Curvature Method,” Journal of Sound and Vibration, 226, pp. 1029-1042, 1999.
[29]Warren S. McCulloch and Walter Pitts, “A Logical Calculus of the Ideas Immanent in Nervous Activity,” Bulletin of Mathematical Biology, Vol.5, No.4, pp.115-133, 1943.
[30]Widrow, B., “Reliable, Trainable Networks for Computing and Control,” Standford University, 1962.
[31]Werner Soedel, “Vibrations of Shells and Plates,” Marcel Dekker, America, 1993.
[32]Wang, Q., Deng, X., “Damage Detection with Spatial Wavelets,” International Journal of Solids and Structures, Vol.36, pp.3443-3468, 1999.
[33]Yam, L.H., Yan, Y.J. and Jiang, J.S., “Vibration-Based Damage Detection for Composite Structures Using Wavelet Transform and Neural Network Identification,” Composite Structures, Vol.60, Issue 4, pp. 403-412, 2003.
[34]Yam, L.H., Yan, Y.J., Cheng, L. and Jiang, J.S., “Identification of Complex Crack Damage for Honeycomb Sandwich Plate Using Wavelet Analysis and Neural Networks,” Smart Materials and Structures, Vol.12, No.5, pp.661-671, 2003.
[35]Yang, J.M., Hwang, C.N., and Yang, B.L., ”Crack Identification in Beams and Plates by Discrete Wavelet Transform Method, ” Journal of Ship Mechanics, Vol.3, No.3, pp.464-472, 2008.
[36]Zang, C., Imregun, M., “Structural Damage Detection Using Artificial Neural Networks and Measured FRF Data Reduced Via Principal Component Projection,” Journal of Sound and Vibration, Vol.242, No.5, pp.813-827, 2001.
[37]Zhong, Shuncong, Olutunde Oyadiji, S., “Crack Detection in Simply Supported Beams Without Baseline Modal Parameters by Stationary Wavelet Transform,” Mechanical Systems and Signal Processing, 21, pp.1853-1884, 2007.
[38]胡昌華, 張軍波, 夏軍, 張偉, “基於MATLAB的系統分析與設計：
小波分析,” 西安電子科技大學出版社, 中國大陸, 1999.
[39]林子超, “類神經網路在結構損傷偵測分析的應用,” 國立成功大
學航空太空工程研究所, 碩士論文, 中華民國八十六年六月.
[40]周志豪, “應用類神經網路於主動振動控制之研究,” 南台科技大
學機械工程系研究所, 碩士論文, 中華民國九十五年六月.
[41]長思科技產品研發中心, “MATLAB6.5輔助小波分析與應用,＂
電子工業出版社, 北京, 2003.
[42]許有村, “小波理論在機械結構破壞點偵測上的應用,” 國立台灣
大學機械工程研究所, 碩士論文, 中華民國八十七年六月.
[43]張智傑, “小波訊號處理於結構破損偵測之應用,” 國立成功大學
機械工程學系, 博士論文, 中華民國九十三年六月.
[44]曾韋鳴, “利用類神經網路結合離散小波轉換進行樑與板之破損偵
測,” 國立成功大學機械工程學系, 碩士論文, 中華民國九十九年
六月.
[45]楊澤民, 廖翊宏, 嵇泓鈞, “小波理論應用於樑的破損偵測之究,”
中國造船暨輪機工程學刊, Vol.23, No.4, pp.189-197, 2004.
[46]楊澤民, 黃正能, 柯志宏, 曾韋鳴, “二維離散小波轉換應用於帶
有加強材之平板破損偵測,” 中國造船暨輪機工程學刊, Vol.28,
No.1, pp.29-40, 2009.
[47]楊澤民, 楊正瑋, “小波轉換應用於板架結構的損傷偵測,” 中國造
船暨輪機工程學刊, Vol.28, No.4, pp. 221-235, 2009.
[48]黎文明, “快速傅立葉轉換,” 復漢出版社, 台灣, 1985.
[49]趙景明, 梁淑芳, “導入LM 法之平行倒傳遞演算法,” 資訊管理展
望期刊, Vol. 8, Issue. 2, 2006.
[50]蔡展榮, “小波基礎理論 與應用課程講義,” 國立成功大學空間及
測量工程學系研究所, 2002.
[51]蔡哲緯, “應用類神經網路於結構損傷定位之研究,” 國立成功大
學航空太空工程研究所, 碩士論文, 中華民國九十七年六月.
[52]羅華強, “類神經網路-Matlab的應用,” 高立圖書有限公司, 台灣,
2008.
[53]鐘啟聞, “應用類神經網路與自然頻率於結構物之損壞預測,” 國
立成功大學造船暨船舶機械工程研究所, 碩士論文, 中華民國九
十一年六月.