劉佩玲臺灣大學：應用力學研究所葉柏涼Yeh, Po-LiangPo-LiangYeh2007-11-292018-06-292007-11-292018-06-292006http://ntur.lib.ntu.edu.tw//handle/246246/62577本研究之主旨在發展敲擊回音法之訊號分析方法與影像技術，使量測結果以最簡單、直覺與容易辨識的方式呈現。 敲擊回音法已被廣泛使用於混凝土尺寸及品質檢測，該方法將結構受敲擊後之表面反應進行傅立葉轉換，再由頻率域訊號判讀結構尺寸或缺陷位置。傅立葉轉換的原理是建構於穩定訊號之假設上，而結構受敲擊之反應絕非穩定訊號，其頻率組成會隨時間而改變。因此，本研究對適用於非穩定訊號之時間－頻率域分析進行深入探討，包括短時傅立葉轉換及小波轉換。 為驗證本研究所提出之各種訊號處理方法，我們灌製數個混凝土模型，用以量取各種不同裂縫情況下之訊號，並且利用動態有限元素軟體LS－Dyna來建立與模型試體相同之數值模型，並比較數值模擬與模型試驗結果之差異，以找出適當的模型建立與參數設定步驟，使數值模型能表現出模型試體之特性。數值與實驗結果皆提供後續分析比對使用。 經由數值與實驗數據分析發現，敲擊回音訊號的傅立葉頻譜雖然頻率解析度最佳，但會產生多重尖峰與漣漪現象，短時傅立葉轉換雖可避免漣漪現象，但還是有多重尖峰，小波轉換則無此兩種干擾。時間－頻率域分析的另一優點就是可直接觀察到表面波及模態振動的頻段與時段，因此訊號解讀更不易造成誤判。此外，傅立葉及短時傅立葉轉換的頻率解析度都是固定的，小波轉換則是隨頻率增高，頻率解析度降低。此種特性正好符合敲擊回音試驗的需要，因為深度與頻率成反比，故由頻率尖峰換算成深度時，若希望深度解析度保持一致，頻率解析度就應該隨頻率降低而增加。小波轉換雖然最容易判讀，但頻率解析度不及傅立葉轉換，故進行敲擊回音試驗時，也可取兩者之優點，將小波頻譜與傅立葉頻譜並列，由小波頻譜找到尖峰大略位置之後，再由傅立葉頻譜定出尖峰的頻率值。 為使量測結果以直觀、正確與快速的方式顯示，本研究也發展二維與三維影像技術來呈現分析結果。首先，藉由超音波檢測中的B-Scan與C-Scan概念，將傅立葉頻譜與小波頻譜換算成色階值，再繪製成試體垂直斷面與水平切面影像，接著，又結合兩種轉換法的優點，以組合頻譜繪製垂直及水平斷面影像。最後，本研究運用三維影像技術中面描繪與體描繪技術，將量測數據以最有效直覺的三維圖形呈現。研究中發現，體描繪法較穩定，不易受雜訊影響，而面描繪法若參數設定佳，則比較能表現細部特徵，故試驗時可先以體描繪影像大致了解試體內部之情形，再以面描繪影像觀察細部。 經由數值與實驗驗證，可發現使用組合頻譜影像通常都能得到最好的效果。處理數值訊號時，不論二維或三維影像法都可有效地辨識裂縫位置。若處理實驗訊號，則面描繪影像品質較易受訊號品質影響，若有淺層裂縫時，由於撓曲振動能量太強，必須配合觀察裂縫下方之底部反射方能判斷裂縫位置。在現場進行敲擊回音試驗時，可將本研究所發展之影像法互相搭配使用，以得到較準確之判斷。The impact echo method is widely used in the nondestructive inspection of concrete structures. In the test, an impact is applied on the surface of the concrete structure, and the surface response of the concrete due to the impact is measured and recorded. Then, the Fourier transform is adopted to transform the response from the time domain to the frequency domain. Since interfaces, cracks, or voids will induce multiple reflections and peaks will form in the Fourier spectrum. Hence, the spectrum will reveal the size of the structure or the location of the defect. The theory of Fourier transform is built on the hypothetical assumption of stationary signal. Unfortunately, the impact response of a structure is by no means stationary, and its frequency content varies with time. To take the non-stationary nature of impact signal into account, two time-frequency domain analyses are studied in this research, namely, the short-time Fourier transform and the wavelet transform. To examine the effect of various signal processing methods, several concrete models with imbedded cracks were molded. Finite element models were also constructed to simulate the model tests. The simulation parameters were selected such that the numerical results agreed with the experimental data. The simulation and experiment results were then used to verify and compare the methods proposed in this study. Through theoretical analysis and case study, it is found that the Fourier transform has the best frequency resolution. However, its spectrum possesses multiple peaks and ripples. Such phenomena complicate the diagnosis. The short-time Fourier transform can avoid the ripples, but multiple peaks still exist. The wavelet transform, on the other hand, has neither interferences. The Fourier transform and short-time Fourier transform has fixed frequency resolution, but the frequency resolution of the wavelet transform deteriorates as the frequency increases. Fortunately, this property complies with the need of the impact echo method. Another advantage of the time-frequency analysis is that one can directly detect the surface wave and the modal vibration from the spectrogram of the short-time Fourier transform and the scalogram of the wavelet transform. Since the surface wave and the modal vibration are usually very high in energy, they often cause trouble when deciphering the signals. Although the marginal spectrum of the wavelet transform contains least interference among the three methods and is easy to identify the peak due to the multiple reflections of interface in the concrete, the peak is not as sharp as in the Fourier spectrum. Hence, it is suggested that one first identify the peak in the wavelet spectrum, find the corresponding peak in the Fourier spectrum, and then determine the frequency of the peak using the Fourier spectrum. In order to provide the engineers with a more direct way of detecting the defects in the structure, several imaging methods are developed in this research. The two-dimensional imaging methods adopt the concepts of the B-scan and C-scan in the ultrasonic detection. In the spectral B-scan method, a series of impact echo tests are performed along a line and represent the spectral amplitude of the signals by color scale. Then, an image is constructed using the spectra of the tests with the test position as the horizontal axis and the frequency as the vertical axis. The B-scan image provides the defect information on the vertical section under the test line. The C-scan spectral method, on the other hand, constructs an image for a horizontal section. In the C-scan method, the impact echo tests are performed on an area on the concrete surface. Then, select the depth of the horizontal section to be inspected, and determine the corresponding frequency for the depth. Finally, a spectral image is constructed for the horizontal section by representing the spectral amplitude by color scale. This research also proposes two three-dimensional imaging methods. Similar to the C-scan method, the impact echo tests are performed on an area on the concrete surface. Then, the surface rendering and volume rendering techniques are applied to the spectra of the signals to construct the three-dimensional image of the concrete interior. It is found in the research that the volume rendering method is more stable and is less sensitive to the signal noise. However, the surface rendering method can better exhibit the details of the internal defect. Therefore, one may utilize the volume rendering image to get a rough image of the concrete interior. Then, use the surface rendering method to observe the details. Both numerical simulations and experimental results are used to verify the proposed imaging methods. Three spectra are adopted to construct the images, namely, the Fourier spectrum, the wavelet spectrum, and the product of the two spectra. It is found that image of the product spectrum yields the best results. With the numerical signals, all imaging methods can depict the crack locations effectively. In processing the experimental data, the quality of the images is deteriorated by the existence of the noise, especially the surface rendering method. However, the cracks can still be detected. The imaging methods have difficulty in describing shallow cracks, because the energy of flexural vibration is very strong. In that situation, one may determine the location of the shallow crack by observing the bottom reflection.第一章 前言 1 1-1 研究動機 1 1-2 文獻回顧 3 1-3 本文簡介 7 第二章 敲擊回音法之原理 9 2-1應力波傳行為 9 2-2敲擊回音法 11 2-3敲擊回音試驗參數 14 2-3-1 敲擊源 14 2-3-2 總取樣時間 17 2-3-3 取樣時距 18 2-4傅立葉轉換 19 2-4-1傅立葉轉換原理 19 2-4-2快速傅立葉轉換 20 2-4-3取樣定理(Sampling Theorem) 24 2-5敲擊回音法算例 25 第三章 模型試驗 33 3-1模型試體 33 3-2實驗設備 35 3-3測點佈設 36 3-4實驗參數 36 第四章 有限元素分析 43 4-1 有限元素法分析軟體介紹 44 4-2 有限元素分析步驟 45 4-3 數值算例結果與分析 52 4-3-1數值算例一 52 4-3-2數值算例二 56 4-3-3數值算例三 57 4-3-4數值算例四 58 4-3-5數值算例五 60 4-4 模型試驗與數值模擬之比較 61 4-4-1模型試驗一 62 4-4-2模型試驗二 63 4-4-3模型試驗三 65 4-4-4模型試驗四 66 4-4-5模型試驗五 67 4-5 小結 68 第五章 訊號的時間－頻率域分析 95 5-1傅立葉轉換 97 5-1-1傅立葉轉換的性質 97 5-1-2傅立葉轉換之限制 98 5-2短時傅立葉轉換(SHORT TIME FOURIER TRANSFORM) 98 5-2-1短時傅立葉轉換的邊際頻譜 101 5-2-2短時傅立葉轉換的性質 102 5-2-3短時傅立葉轉換之限制 102 5-3小波轉換(WAVELET TRANSFORM) 103 5-3-1小波轉換的邊際頻譜 106 5-3-2小波函數的性質 107 5-3-3小波轉換的性質 109 5-3-4連續小波函數 109 5-4訊號的測不準原理(UNCERTAINTY PRINCIPLE) 113 5-5 FT、STFT與WT之比較 115 1. 算例一 116 2. 算例二 118 3. 算例三 120 5-6小波轉換在濾波上之應用 122 5-6-1多解析度分析 124 5-6-2離散小波轉換算例 127 5-7敲擊回音法的應用 128 5-7-1傅立葉轉換的缺點 129 5-7-2時間－頻率域分析的優點 132 5-8 數值算例分析 137 5-8-1數值算例一 138 5-8-2數值算例二 141 5-8-3數值算例三 143 5-8-4數值算例四 145 5-8-5數值算例五 147 5-9 模型試驗分析 150 5-9-1 實驗訊號處理 151 5-9-2 模型試驗一 154 5-9-3 模型試驗二 155 5-9-4 模型試驗三 155 5-9-5 模型試驗四 156 5-9-6 模型試驗五 157 5-10小結 159 第六章 頻譜訊號之影像法 231 6-1頻率域二維影像法 231 6-1-1頻率域垂直斷面掃描法 231 6-1-2頻率域水平切面掃描法 234 6-2小波轉換於影像法之應用 235 6-2-1垂直斷面影像 236 6-2-2水平切面影像 239 6-3數值算例之二維影像分析 240 6-3-1數值算例一 241 6-3-2數值算例二 242 6-4模型試驗之二維影像分析 243 6-4-1模型試驗一 244 6-4-2模型試驗二 245 6-4-3模型試驗三 245 6-5頻率域三維影像 246 6-5-1 資料視覺化 246 6-5-2 三維影像 247 6-5-3 三維影像程式 250 6-6數值算例之三維影像分析 251 6-6-1數值算例一 251 6-6-2數值算例二 253 6-6-3數值算例三 253 6-7模型試驗之三維影像分析 254 6-7-1模型試驗一 254 6-7-2模型試驗二 254 6-7-3模型試驗三 255 6-8小結 255 第七章 結論與展望 303 參考文獻 309en-US非破壞檢測敲擊回音有限元素時頻分析小波影像三維NDTImpact echoFinite element methodTime-frequency analysisWaveletImage3Dthesis