應用應力波傳理論檢測基樁完整性，本研究目的為推估現地大型基樁之樁長，為提高分析結果的準確率，透過音波回音法加上不同類型之複數小波轉換，以過往的現地試驗之數據作分析，討論其結果是否準確，常見的複數小波類型有Shannon、Morlet、Gaussian、Frequency B-Spline，小波的選擇通常依資料型態而定，實際使用上則需經過測試始知是否合適，原則上高頻訊號需使用較高頻的小波，本研究使用Morlet和Gaussian複數小波進行分析，另外，小波參數之選擇，需使分析結果能清楚辨識特徵訊號處、振幅頻譜尖銳。
試驗之基樁長度分別為28 m、34 m、38 m、53 m，透過小波轉換後的振幅頻譜和相位頻譜，來推估基樁之樁長。另外，同時也探討使用不同類型之小波時對於分析結果之影響，如Gaussian和Morlet。結果顯示，樁長檢測使用音波回音法搭配複數Morlet小波轉換，均能準確推估基樁的長度；當使用複數Gaussian小波時，較高的頻率使其相位頻譜更為複雜，讓53 m樁長分析較為困難，而50 m以下仍能準確評估。

By applying stress wave theory to detect pile integrity, the purpose of this study is to estimate the pile length of large-scale and in-situ piles. In order to improve the accuracy of the analysis results of sonic echo (SE) method and different wavelet functions. The common complex wavelets include Shannon, Morlet, Gaussian, and Frequency B-Spline. The choice of mother wavelet depends on the data type and user experience. The complex Morlet and the complex Gaussian wavelets are used in this study. The wavelet parameters must make the characteristics of the signal clearly, and the amplitude spectrum sharp.

The length of the tested piles are 28 m, 34 m, 38 m, and 53 m, and the length of the pile is estimated by the amplitude spectrum and phase spectrum after wavelet transform. In addition, we also discuss differences between wavelet functions for the analysis, such as Gaussian, and Morlet. The results show that the length of the pile can be estimated accurately by using the sonic echo method with complex Morlet wavelet transform. When the complex Gaussian wavelet is used, the pile under 50 m is easy to detect accurately, however, the high frequency wavelet makes the phase spectrum more complicated, and the pile over 50 m is difficult to detect accurately.

1. 王志坤，「基於小波振幅頻譜和複小波相位頻譜的高分辨率層序劃分」，石油學報，第29卷，第6期，第865-869頁。（2008）
2. 尹繼堯、劉明高、趙建章，「利用時頻域地震信號相位殘點特徵檢測地層連續性」，石油地球物理勘探，第49卷，第4期，第745-750頁。（2014）
3. 李允仲，「音波回音法應用於基樁完整性檢測之實驗研究」，碩士論文，國立成功大學土木工程研究所。（2009）
4. 李青鋒，「連續複小波變換在工程檢測數據處理中的應用」，中國礦業大學學報，第36卷，第1期，第23-26頁。（2007）
5. 李俊男，「脈波反應法應用於基樁之模擬與分析」，碩士論文，國立成功大學土木工程研究所。（2005）
6. 吳多詠，「平行震測法應用於含樁帽基樁長度檢測之研究」，碩士論文，國立成功大學土木工程研究所。（2011）
7. 周暐翔，「複數連續小波轉換應用於基樁完整性檢測之研究」，國立成功大學土木工程研究所。（2015）
8. 呂佳蓉，「小波分析應用於基樁脈波反應檢測」，碩士論文，國立成功大學土木工程研究所。（2012）
9. 林宜清，「應力波檢測技術及應用」，第八屆公共工程非破壞檢測技術研討會，第59-81頁。（2013）
10. 倪勝火、羅國峯，「小波轉換法應用於基樁音波回應法之分析研究」，中華民國非破壞檢測協會，第19卷，第1期，第4-15頁。（2001）
11. 倪勝火、廖述濤，「基樁之檢測與評估」，第一屆公共工程非破壞檢測技術研討會，台北，第156-215頁。（1999）
12. 陳振國，「總體經驗模態法應用於基樁完整性檢測之研究」，碩士論文，國立成功大學土木工程研究所。（2017）
13. 陳乙豪，「音波回音法與脈波反應法應用於基樁非破壞性檢測之可行性分析」，碩士論文，國立成功大學土木工程研究所。（2015）
14. 黃烟宏，「連續小波轉換應用於基樁完整性檢測之研究」，碩士論文，國立成功大學土木工程研究所。（2006）
15. 黃烟宏，「應力波應用於樁基礎完整性檢測技術之評估」，博士論文，國立成功大學土木工程研究所。（2011）
16. 蔡靖、王建華、張獻民，「小波變換在確定樁裂縫、斷樁及淺部缺陷中的應用」，岩土力學，第28卷，第3期，第565-569頁。（2007）
17. 潘貝咏，「希伯特-黃轉換於含樁帽基樁非破壞檢測之應用」，碩士論文，國立成功大學土木工程研究所。（2015）
18. 賴正昇，「脈波回音法應用於基樁之模擬與分析」，碩士論文，國立成功大學土木工程研究所。（2005）
19. 羅國峯，「大型基樁完整性檢測之試驗與分析」，博士論文，國立成功大學土木工程研究所。（2007）
20. Addison, P.S., and Watson, J.N. (2002), “Low-oscillation complex wavelets,” Journal of Sound and Vibration, Vol. 254, No. 4, pp. 733-762.
21. Bolt, B.A. (1993), Earthquake and Geological Discovery, Scientific American Library, New York.
22. Davis, A.G. (2003), “The nondestructive impulse response test in north America: 1985–2001.” NDT & E International., Vol. 36, pp. 185-193.
23. Davis, A.G. (1974), “From theory to field experience with the non–destructive vibration testing of piles,” Proceedings Institute of Civil Engineering, Part 2, 57, pp. 571–593.
24. Daubechies, I. (1992), “Ten lectures on wavelets,” CBMS-NSF Regional
Conference Series in Applied Mathematics, SIAM, Vol. 61
25. Huang, N.E., Shen, Samuel S.P. (2005), Hilbert-Huang Transform and Its Applications, Word Scientific Inc., New Jersey.
26. Jiang, X., and Ma, Z.J. (2012), “Crack detection from the slope of the mode shape using complex continuous wavelet transform,” Computer-Aided Civil and Infrastructure Engineering, Vol. 27, pp. 187-201.
27. Lin, J.M., and Sansalone, M. (1994), “Impact echo response of hollow cylindrical concrete structures surrounded by soil and rock: part I--numerical studies,” Geotechnical Testing Journal, Vol. 17, No. 2, pp. 207-219.
28. Mohd, S., and Holford, K.M. (2012), “Acoustic emission source location in steel structures using a wavelet transform analysis and modal location theory,” Proceedings of 30th European Conference on Acoustic Emission Testing, pp. 12-15.
29. Misiti, M., Misiti, Y., Oppenheim, G., and Poggi, J.M. (2015), Wavelet Toolbox: User’s Guide.
30. Nesvijski, E. (2007), “Wavelet transform and its applications to acoustic emission analysis of asphalt cold cracking,” NDT.net, Vol. 12, No. 6, pp 1-13.
31. Park, H.C., and Kim, D.S. (2006), “Non-destructive pile integrity test using HWAW method,” Key Engineering Materials, Vols. 321-323, pp. 363-366.
32. Richart Jr, F.E., Hall Jr, J.R., and Woods, R.D. (1970), Vibrations of Soils and Foundations, Prentice-Hall, Inc.
33. Steinbach, J., and Vey, E. (1975), “Caisson evaluation by stress wave propagation method,” Journal of Geotechnical Engineering Division, ASCE, Vol. 101, No. GT4, pp. 361-387.
34. TNO Building and Construction Research (1997), Foundation Pile Diagnostic System: Sonic Integrity Testing, Netherland.
35. Woods, R.D. (1968), “Screening of surface waves in soils,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 94, No. SM4, pp. 951-979.
36. Wu, Z. (2014), “Detection and localization of power quality disturbances based on complex wavelet,” Journal of Electrical Engineering, Vol. 2, No. 2, pp. 9-17.
37. Wigner, E.P. (1932), “On the quantum correction for thermodynamic equilibrium,” Phys. Rev., Vol. 40, pp. 749-759.
38. Yeh, P.L., and Liu, P.L. (2008), “Application of the wavelet transform and the enhanced fourier spectrum in the impact echo test,” NDT & E International, Vol. 41, No. 5, pp. 382-394.