傳統上，結構物損傷非破壞檢測，大多使用快速傅立葉轉換(Fast Fourier Transform)，但傅立葉方法以不隨時變的諧和函數作為基底函數來處理訊號，不符合非線性與非穩態系統訊號的基本要求。本研究以使用商業軟體ABAQUS建立三組不同損害程度的結構模型，地震力使用集集地震與花蓮外海地震進行動力分析試驗，利用希爾伯特-黃轉換(Hilbert-Huang Transform，HHT)的時頻分析技術，其具有局部隨適性與後待定基底函數兩個特性，定義上符合非穩態系統(Non-stationary System)的基本要求，常用於非穩態與非線性訊號資料分析上。從時頻譜可以看出訊號在時間域與頻率域上的能量分布，觀察到譜上能量會集中於某固定頻率值，可視為該結構模態的主頻，還可以觀察到物體隨時間變化的動態特性。
研究方法使用HHT SHM分析方法中時頻放大函數T.F.AF與模態時間曲線MTVC兩個分析工具。T.F.AF將原始資料波形先轉換成波傳特性展現，結構受震時各波向動力特性可清楚展現出來。觀察時頻譜上能量與瞬時頻率的分布，於T.F.AF頻譜中擷取振動模態特質稱為模態時間曲線，在MTVC中可觀察到結構的安全參數訊息，藉由不同試驗條件，觀察結構特質的變化找出結構模態行為的細微差異，分析結構物受震後的結構安全狀態。

Traditionally, Nondestructive Testing of structural damage has mostly used Fast Fourier Transform, Fourier analysis using time invariant harmonic function as a basis function which is unable to meet the basic requirements of nonlinear and non-stationary signals. The commercial software ABAQUS was used in this research. Three sets of structural models with different degrees of damage were established. Earthquake history using Chi-Chi earthquake and Hualien offshore earthquake for dynamic analysis. The Hilbert Huang Transform (HHT), which is a time frequency analysis technique without a prior basis functions and local adaptability, the time-variant characteristic of the Hilbert Transform makes the analysis for the non-stationary system possible, is often used for nonlinear and non stationary signal analysis. From the time frequency spectrum, catching sight of the energy distribution of the signal in the time domain and the frequency domain. It is observed that the energy on the time frequency will be concentrated on a fixed frequency value, which can be regarded as the dominant frequency of the structural mode, and the dynamic characteristics of the structural as a function of time can also be observed.
This study uses two analysis tools of the HHT SHM analysis method, the time-frequency amplification function (T.F.AF) and the modal time curve (MTVC). T.F.AF converts the raw data into a wave propagation characteristic, the dynamic characteristics of each phase of the structure will be apparently exhibited. Observing the distribution of energy and instantaneous frequency on the time frequency spectrum, and then the vibration mode characteristic in the T.F.AF spectrum is called MTVC. Observing the structural safety parameter information from the MTVC. Using different conditions, one can observe structural traits and find subtle differences in structural modal behavior which can be utilized to analyze the structural safety after earthquake.

1. 蘇聖中，「結構物強震觀測資料之希爾伯特-黃結構健康診斷方法」國立中央大學，博士論文，民國104年。
2. Rytter A., “Vibration based inspection of civil engineering structures”. h.D.Dissertation, Department of Building Technology and Structural Engineering,Aalborg University, Denmark, 1993.
3. Wu, Z., and N. E. Huang, “A Study of the Characteristics of White Noise Using the Empirical Mode Decomposition Method”, Proc. Roy. Soc. London, Vol. 460A, pp. 1597-1611, The Royal Society, June 2004.
4. 劉德俞，「應用希爾伯特黃轉換方法改進結構系統識別方法於橋梁振動訊號之研究」國立中央大學，博士論文，民國 100 年。
5. Gabor D. 1946, Theory of communication. Proc. IEE 93, 429-457.
6. Ibrahim S. R., Sept-Oct. 1978, “Modal Confidence Factor in Vibration Testing”, Journal of Spacecraft and Rockets, Vol. 15, pp. 313-316.
7. Ibrahim S. R., and Mikulcik E. C., Aug. 1976, “A Method for the Direct Identification of Vibration Parameters from the Free Responses”, Shock and Vibration Bulletin, Vol. 47, Pt. 4, pp. 183-198.
8. 黃進國，「梁結構損傷偵測」，國立中央大學，博士論文，民國98 年。
9. Broclcwell, P. J., and Davis R. A.. 1991, “Time Series: Theory and Methods,” Springer-Verlag. New York.
10. Newland D. E. 1993, “An introduction to Random Vibrations, Spectral and Wavelet Analysis,” John Wiley & Sons, Inc., New York.

11. Huang, N. E., Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, H. H. Liu, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis”, Proc. Roy. Soc. Lond., Vol. 454A, pp. 903-993, The Royal Society, March 1998.
12. Wu Z. H. and Huang N. E., 2005, “Ensemble empirical mode decomposition: A noise-assisted data analysis method,” Center for Ocean-Land-Atmosphere Studies, Technical Report series, Vol. 193, No.173.
13. Wu Z. H. and Huang N. E., 2009, “Ensemble Empirical Mode Decomposition: a noise-assisted data analysis method,” Advances in Adaptive Data Analysis, Vol. 1, No. 1, pp. 1–41
14. Cohen L. 1995, Time-frequency analysis. Englewood Clips, NJ: Prentice-Hall.
15. Gabor D. 1946, Theory of communication. Proc. IEE 93, 429-457.
16. Titchmarsh E. C. 1948 Introduction to the theory of Fourier integrals. Oxford University Press.
17. 混凝土鋼橋一般檢測手冊，台灣省住宅及都市發展局，民國84年。
18. Wu, Z., and N. E Huang, “Ensemble Empirical Mode Decomposition: A Noise-Assisted Data Analysis Method”, Advances in Adaptive Data Analysis. Vol.1 No.1, pp. 1-41, World Scientific, January 2009.
19. Norden E. Huang, Kang Huang and Wei-Ling Chiang, “HHT-BASED BRIDGE STRUCTURAL HEALTH-MONITORING METHOD”
20. Borcherdt, R. D., “Effects of Local Geology on Ground Motion near San Francisco Bay.”, Bull. Seism. Soc. Am, Vol, 60 No. 1,pp.29-61, Seismological Society of America, February 1970
21. 李仁杰、張晉昌，「砂模鑄造能力本位訓練教材-非破壞性檢測滲透檢測（PT）」中華民國職業訓練研究發展中心，民國90年12月。
22. 李有豐，「橋梁檢測評估與維修人員訓練講習班論文集」，第七章 非破壞檢測與評估第7-1~7-61頁，交通部運輸研究所，台北，民國89年8月。
23. 蕭勇順，「以超音波量測混凝土的強度」檢測科技，民國78年。
24. 劉正偉，「梁構件系統之識別參數與損傷檢測之應用」國立中央大學，碩士論文，民國93年。
25. Zhang, R. R, R. King, L. Olson and Y. L. Xu, “Dynamic Response of the Trinity River Relief Bridge to Controlled Pile Damage: Modeling and Experimental Data Analysis Comparing Fourier and Hilbert-Huang Techniques”, Journal of Sound and Vibration, Vol. 285 issue 4-5, pp. 1049-1070, Elsevier Ltd., August 2005.
26. Tang J. P. and Leu K. M. 1991, “Vibration Test and Damage Detection of P/C Bridge “, Journal of Chinese Institute of Engineers. Vol. 14, No. 5, pp. 531-536.
27. Ito Y. and Uomoto T., 1997, “Nondestructive testing method of concrete using impact acoustics”, NDT&E International, Vol. 30, No. 4, pp217-222
28. Wu T. C., Loh C. H. , Hunag N. E. 2000, “Application of EMD+HHT Method to Seismic Response Data of Bridge Structure", Second international workshop on mitigation of seismic effects on transportation structures, Sep 13-15.
29. Juang J. N., Cooper J. E. and Wright J. R., Mar. 1988, “An Eigensystem Realization Algorithm using Data Correlations(ERA/DC) for Modal Parameter Identification”, Control-Theory and Advanced Technology, Vol. 4, No. 1, pp. 5-14.
30. 陳宏南，「希爾伯特頻譜於橋梁非破壞檢測之應用」，國立中央大學，碩士論文，民國90年。
31. 張奕翔，「應用HHT-SHM法於單塔脊背橋結構健康監測」，國立中央大學，碩士論文，民國107年。
32. 莊靜怡，「應用HHT頻譜於結構物地震損傷之研究，國立中央大學，碩士論文，民國98年。
33. Huang N. E and Shen S. P. 2005, “Hilbert-Huang Transform and Its Applications”, World Scientific Publishing Co., Ch. 12, pp. 305-334.
34. Loh C. H., Wu T. C. and Huang N. E., “Application of the Empirical Mode Decomposition-Hilbert Spectrum Method to Identify Near-Fault Ground-Motion Characteristics and Structural Responses”, Bulletin of the Seismological Society of America, 91.5. pp. 1339-1357. October, 2001.
35. Cohen L. 1995, Time-frequency analysis. Englewood Clips, NJ: Prentice-Hall.
36. Norden E. Huang, “Degree of Nonlinearity Quantifying Nonlinearity”