本論文針對新建初完工的單塔脊背橋，利用全橋動態車載試驗，分析橋梁結構放大特性，而橋梁結構受振反應往往具有非線性及非穩態性，在傅利葉上使用不隨時變的諧和函數作為基底函數的訊號處理方法，不符合非線性與非穩態系統訊號的基本要求。為了進行橋梁損傷的非破壞檢測，利用希爾伯特-黃轉換(Hilbert-Huang Transform，HHT)新穎的時頻分析技術，其具有後待定基底函數與局部隨適性的特性，常用於非線性且非穩態訊號分析上，可展現訊號在時間域與頻率域上的能量分布，觀察物體隨時間變化之動態特性。來分析結構物經動態車載試驗資料，探討橋梁結構受震後的結構安全狀態，並借助瞬時頻率來解讀結構體振動特性變化。
研究方法為HHT SHM分析法，其中兩個分析工具，時頻放大函數T.F.AF與模態時間曲線MTVC。將外力波形轉換成波傳特性相關展現，結構受震時各波相動力特性會在T.F.AF上展現出來，透過觀察時頻譜上能量與瞬時頻率的分布，找出時變系統振動行為，接著於T.F.AF頻譜中擷取振動模態特質稱為MTVC。MTVC中有豐富的結構安全參數訊息，比對不同試驗條件，估算結構特質的變化情形找出結構模態行為的細微差異。

This study uses Dynamic Vehicle Test to analyze the amplification characteristics of the bridge structure which is just completed. However, the bridge structure responses of vibration are often nonlinear and non-stationary. Fourier analysis using time invarint harmonic function as a basis function which is unable to meet the basic requirements of nonlinear and non-stationary signals. In order to carry out non-destructive testing of bridge damage, the Hilbert-Huang Transform (HHT), which is a time-frequency analysis technique without a prior basis functions and local adaptability, is often used for nonlinear and non-stationary signal analysis, it can show the energy distribution of the signal in the time domain and frequency domain and observe the dynamic characteristics of the object changing with time.
This study uses two analysis tools of the HHT SHM analysis method, the time-frequency amplification function (TFAF) and the modal time curve (MTVC). Converting the external force waveform into a wave-propagation characteristic, the dynamic characteristics of each phase of the structure will be exhibited on the TFAF, and the time-varying system vibration behavior will be found by observing the distribution of energy and instantaneous frequency on the frequency spectrum, and then the vibration mode characteristic in the TFAF spectrum is called MTVC. MTVC has a wealth of structural safety parameter information. It compares the external conditions of different tests, estimates structural traits and finds subtle differences in structural modal behavior.

1. 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。
2. Norden E. Huang, Kang Huang and Wei-Ling Chiang,“HHT-BASED BRIDGE STRUCTURAL HEALTH-MONITORING METHOD”
3. 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。
4. 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。
5. 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。
6. 蕭勇順，「以超音波量測混凝土的強度」檢測科技，民國78年。
7. 劉傳騰，「橋梁動態載重識別之模態函數法」國立中央大學，碩士論文，民國103年。
8. 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。
9. Cohen, L., “Time-frequency Analysis”, Prentice-Hall, New York, USA, December 1994
10. 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.
11. 黃進國，「梁結構損傷偵測」，國立中央大學，博士論文，民國 98 年。
12. Broclcwell, P. J., and Davis R. A.. 1991, “Time Series: Theory and Methods,” Springer-Verlag. New York.
13. Newland D. E. 1993, “An introduction to Random Vibrations, Spectral and Wavelet Analysis,” John Wiley & Sons, Inc., New York.
14. 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.
15. 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..
16. 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
17. Tang J. P. and Leu K. M. 1991, “Vibration Test and Damage Detection of P/C Bridge “, Journal of Chinese Institude of Engineers. Vol. 14, No. 5, pp. 531-536.
18. Ito Y. and Uomoto T., 1997, “Nondestructive testing method of concrete using impact acoustics”, NDT&E International, Vol. 30, No. 4, pp217-222
19. 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.
20. 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.
21. 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。
22. Huang N. E and Shen S. P. 2005, “Hilbert-Huang Transform and Its Applications”, World Scientific Publishing Co., Ch. 12, pp. 305-334.
23. 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.
24. Cohen L. 1995, Time-frequency analysis. Englewood Clips, NJ: Prentice-Hall.
25. Gabor D. 1946, Theory of communication. Proc. IEE 93, 429-457.
26. Titchmarsh E. C. 1948 Introduction to the theory of Fourier integrals. Oxford University Press.
27. 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.
28. 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.
29. 黃炳勳、陳新之、蔣啟恆、陳傳興、劉珊、陳明谷，「大地美脊工藝─脊背橋」台灣世曦，中華技術專題報導No.115，民國106年。
30. 「西濱快速公路54K+320~60K+312(WH10-A)標 UB16箱型梁預力設計書(含橫向預力)」德昌營造股份有限公司，民國104年。
31. Norden E. Huang, “Degree of Nonlinearity Quantifying Nonlinearity”
32. Huang, N. E., M. T. Lo, Z. H. Wu, and X. Y. Chen, “Method for Quantifying and Modeling Degree of Nonlinearity, Combined Nonlinearity and Nonstationarity”, United States Patent Application, Pub. No. US 20130080378A1, 2013.