基樁的非破壞性檢測技術在傳統的訊號理分析方式常利用快速傅立葉轉換(FFT)，然而在轉換過程中常因為FFT的限制造成訊號轉換至頻率域常常發生失真及漏失的現象，因此傳統的基樁缺陷分析方式在尋找缺陷比小於10%的缺陷是困難的。近年來，小波轉換技術已純熟於應用在各種領域的訊號處理上，基樁的非破壞性檢測也是如此。然而早前的小波轉換應用多著重於訊號濾波或時頻圖分析上，對於樁缺陷判斷效果不彰，因此本文分別利用離散小波轉換(DWT)進行訊號判釋應用在脈波反應法(IR method)以及複數連續小波轉換(CCWT)進行時頻分析計算出不同頻帶下之相位-時間關係圖，試圖更準確地找出基樁缺陷的位置。結果顯示，利用DWT應用在脈波反應法上可以系統性地找到缺陷比10%的缺陷，但繁複的分析程序相對於傳統IR法冗長耗時；使用CCWT進行時頻分析則相對簡單且快速，除了保留連續小波轉換(CWT)能提供在不同頻帶上的高解析度外，利用相角圖判斷反射波位置及其代表意義也變得更加簡單。

The purpose of this research is to study in defect detecting for the concrete piles, offering the NDT methods to find out the defects whose size are less than 10%. The restriction of the signal analysis for traditional reflection method is that the small defects are not easy to be found. In this research, there are two ways to detect the defects of pile. The first method, the discrete wavelet transform (DWT) is applied in IR method. The results show that the defect is determined by introducing the DWT based procedure which would reduce the effects of the noise and clarify the signals in frequency domain, and thus it can improve the reliability of the evaluated small defect. Therefore, the resolution of the reflection signals on the defect and the constrained media would be increased when the DWT is introduced into the IR method.
Second method is about using complex continuous wavelet transform (CCWT) to determine pile length and locations of defects on pile foundations by analyzing the time-frequency analysis in different frequency bands. The results show that complex continuous wavelet transform is not only able to provide high resolution results in different frequency bands, which are similar to those bands used by CCWT, but also simplifies the identification of the reflection of the defects. The location of the defects can then be easily determined by utilizing the analyzed phase diagram under the corresponding specific frequencies.

1. 王志坤、鐘建華，「基於小波振幅譜和複小波相位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. 王裕賢，「以連續小波轉換分析土層表面波波速之研究」，碩士論文，朝陽科技大學營建工程研究所。（2010）
3. 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）
4. 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）
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. 周暐翔，「複數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。（2016）
7. 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）
8. 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）
9. 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）
10. 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）
11. Addison, P.S., The Illustrated Wavelet Transform Handbook, Institute of Physics, CRC Pr I Llc. (2002)
12. Baker Jr., C.N., Drumright, E.E., Mensah, F., Parikh, G., and Ealy, C., “Use of nondestructive testing to evaluate defects in drilled shafts,” Transportation Research Record, Vol. 1331, pp. 28-35. (1991)
13. Berger, J.A. and Cotton, D.M., “Low strain integrity testing of deep foundations,” Proceedings of the Fifth Annual Members' Conference, Seattle. (1990)
14. Bolt, B.A., Earthquake and Geological Discovery, Scientific American Library, New York. (1993)
15. Briaud, J.L., Ballouz, M., and Nasr, G., “Defect and Length Predictions by NDT Methods for Nine Bored Piles,” International Perspective on Theory, Design, Construction, and Performance, Orlando, Florida, United Sates, pp. 173-192. (2002)
16. Daubechies, I., Ten lectures on wavelets, SIAM, Philadelphia, pp. 129-131. (1992)
17. Davis, A.G., and Dunn, C.S., “From theory to field experience with the nondestructive vibration testing of piles,” Proceedings, Institute of Civil Engineering, Part 2, 57, Dec., pp. 571-593. (1974)
18. Fei, K., Liu, H.L., and Zhang, T., “Three-dimensional effects in low strain integrity test of PCC pile,” Rock and Soil Mechanics 28:1095–1102. (2007)
19. Finno, R.J. and Gassman, S.L., “Evaluation of bridge foundations by impulse response methods,” Structural Materials Technology III, San Antonio, Texas, United States, pp. 32-43. (1998)
20. Finno, R.J. and Gassman, S.L., “Impulse response evaluation of drilled shafts,” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 124, No. 10, pp. 965-975. (1998)
21. Harrell, A.S. and Stokoe, K.H., II, Integrity Evaluation of Drilled Piers by Stress Waves, Transportation Research Center, The University of Taxes at Austin, pp. 265-268. (1984)
22. Hartung, M., Meier, K., and Rodatz, W., “Integrity testing on model pile,” Proceedings of the Fourth International Conference on the Application of Stress-Wave Theory to Piles, Netherlands, pp. 265-271. (1992)
23. Hertlein, B., and Davis, A.G., Nondestructive Testing of Deep Foundations, John Wiley & Sons, Inc., Chichester, England. (2006)
24. Higgs, J.S., “Integrity testing of concrete piles by shock method,” Concrete, Oct., pp. 31-33. (1979)
25. Huang, Y.H., Ni, S.H., Charng, J.J., and Lo, K.F., “Assessment of identifiable defect size in a drilled shaft using sonic echo method: numerical simulation,” Computers and Geotechnics, 37(6), 757-765. (2010)
26. Hwang, H.J., and Park, H.C., “Evaluation of condition of gravel ballast layer on high-speed railway using surface wave method based on harmonic wavelet analysis of waves.” NDT&E International, Vol. 68, pp. 78-87. (2014)
27. Iskander, M., Roy, D., Kelley, S., and Ealy, C., “Drilled Shaft Defects: Detection, and Effects on Capacity in Varved Clay,” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 129, No. 12, pp. 1128-1137. (2003)
28. Jiang, X., Ma, Z.J., and Ren, W.X., “Crack detection from the slope of the mode shape using complex continuous wavelet transform,” Computer-Aided Civil and Infrastructure Engineering, 27, pp. 187-201. (2012)
29. Kim, D.S., Kim, H.W., and Kim, W.C., “Parametric study on the impact-echo method using mock-up shafts,” NDT&E International, Vol. 35, No. 8, pp. 595-608. (2002)
30. Kinsler, L.E., Frey, A.R., and Coppens, A.B., Fundamentals of Acoustics, John Wiley & Sons., Inc., New York. (1999)
31. Liao, S.T., and Roesset, J.M., “Dynamic response of intact piles to impulse loads,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 21, No. 4, pp. 255-275. (1997)
32. Lin, Y., Sansalone, M., and Carino, N.J., “Impact echo response of concrete shafts,” Geotechnical Testing Journal, Vol. 14, No. 2, pp. 121-137. (1991)
33. Malhotra, V.M., Testing Hardened Concrete: Nondestructive Methods, Iowa State University Press. (1976)
34. Mallat, S., A Wavelet Tour of Signal Processing. Academic, San Diego, 2nd edition. (1999)
35. Misiti, M., Misiti, Y., Oppenheim, G., Poggi, J.-M., Wavelets and their Applications, ISTE USA. (2007)
36. Morlet, J., and Grossmann, A., “Decomposition of hardy functions into square integrable wavelets of constant shape.” SIAM Journal on Mathematical Analysis, Vol. 15, pp. 723-736. (1984)
37. Newland, D.E., “Ridge and phase identification in the frequency analysis of transient signals by harmonic wavelets,” J. Vib. and Acoustics, Trans. ASME, Vol. 121. (1999)
38. Ni, S.H., Huang, Y.H., Lo, K.F., and Charng, J.J., “Estimating the flaw size in drilled shafts using an impulse response method,” KSCE Journal of Civil Engineering. (2011)
39. Ni, S.H., Isenhower, W.M., and Huang, Y.H., “CWT technique for low-strain integrity testing of deep drilled shafts.” Journal of GeoEngineering, Vol. 7, pp. 97-105. (2012)
40. Ni, S.H., Li, J.L., Yang, Y.Z., and Yang, Z.T.. “An improved approach to evaluating pile length using complex continuous wavelet transform analysis.” Insight - Non-Destructive Testing and Condition Monitoring (The Journal of the British Institute of Non-Destructive Testing), Vol. 59, No. 6, pp. 1-7. (2017)
41. Ni, S.H., Lo, K.F., Lehmann, L., and Huang, Y.H., “Time–frequency analyses of pile-integrity testing using wavelet transform.” Journal of Computers and Geotechnics, Vol. 35, pp. 600-607. (2008)
42. Ni, S.H., Yang, Y.Z., and Lyu, C.R., “Application of wavelet analysis for the impulse response of pile,” Smart Structures and Systems, Vol. 19, No. 5, pp. 513-521. (2017)
43. Ni, S.H., Yang, Y.Z., Tsai, P.H., Chou, W..H., “Evaluation of pile defects using complex continuous wavelet transform analysis,” NDT & E International, Vol. 87, pp. 50-59. (2017)
44. Olson, L.D., and Wright, C.C., “Nondestructive testing of deep foundations with sonic methods.” In Kulhawy F.H., editor. Proc Foundation Engineering Congr: Current Principles and Practices. Reston, ASCE, Vol. 2, pp. 1173-1183. (1989)
45. Ovanesova, A.V., and Suarez, L.E., “Application of wavelet transform to damage detection in frame structures.” Engineering Structures, Vol. 26, pp. 39-49. (2004)
46. Park, H.C., and Kim, D.S., “Evaluation of the dispersive phase and group velocities using harmonic wavelet.” NDT&E International, Vol. 34, pp. 457-467. (2001)
47. Park, H.C., and Kim, D.S., “Non-destructive pile integrity test using HWAW method,” Key Engineering Materials, Vols. 321-323, pp. 363-366. (2006)
48. Park, H.C., Kim, D.S., Kim, J.T., Bang, E.S., and Yoon, J.K., “Site characterization using harmonic wavelet analysis of wave (HWAW) method.” 6th International Conference & Exposition on Petroleum Geophysics, pp. 988-995. (2006)
49. Richart Jr, F.E., Hall Jr, J.R., and Woods, R.D., Vibrations of Soils and Foundations, Prentice-Hall, Inc.. (1970)
50. Sarhan, H.A., O'Neill, M.W., and Hassan, K.M., “Flexural performance of drilled shafts with minor flaws in stiff clay,” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 128, No. 12, pp. 974-985. (2002)
51. Stain, R.T., “Integrity Testing,” Civil Engineering, pp. 53-59. (1982)
52. Steinbach, J., and Vey, E., “Caisson evaluation by stress wave propagation method,” Journal of Geotechnical Engineering Division, ASCE, Vol. 101, No. GT4, pp. 361-387. (1975)
53. The Math Works Inc. Wavelet Toolbox for use with Matlab: User’s Guide. (1996)
54. TNO Building and Construction Research, Foundation Pile Diagnostic System: Sonic Integrity Testing, Netherland. (1997)
55. Watson, J.N., and Addison, P.S., “Spectral-temporal filtering of NDT data using wavelet transform modulus maxima.” Mechanics Research Communications, Vol. 29, pp. 99-106. (2002)
56. Woods, R.D., “Screening of surface waves in soils,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 94, No. SM4, pp. 951-979. (1968)