希爾伯特黃轉換於樑上之破壞檢測分析

Crack detection on beams by Hilbert-Huang transform of transient flexural waves

林正偉(Cheng-Wei Lin)

指導教授 ： 王昭男

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.02243

摘要

結構的損傷預測一直是工業界的重要課題，要達到這個目的，必需有適當的訊號處理方法，近年來迅速發展的希爾伯特黃轉換(Hilbert-Huang Transform, HHT)可能提供了一個有效的訊號分析方法。本文討論一維細長方樑上之彎曲波振動訊號，以HHT進行分析，判斷結構是否損壞，並推估其位置。首先，介紹HHT的基本理論，其使用經驗模態分解法，以訊號本身隨時間變化的時間尺度來提出基底，能夠用於非線性與非穩態之訊號分析。接著探討彎曲波之Bernoulli-Euler theory和Timoshenko theory的差異，並計算波速得知彎曲波為頻散波。在實驗部份，選用鋁合金、黃銅以及不鏽鋼作為實驗材料，樑經敲擊產生彎曲波，量測得到加速度訊號，再由 HHT得到時頻圖，從圖上能辨識出邊界反射波和缺陷反射波之峰值，並分別探討波速之計算和缺陷發生位置，而實驗結果得到之誤差(Absolute relative error)平均值皆不超過2.5％。此外，若缺陷深度較深，在時頻圖上之反射波振幅也會較大，可以作為破壞程度之參考依據。

關鍵字

破壞檢測 ； 希爾伯特黃轉換 ； 經驗模態分解法 ； 彎曲波 ； 頻散波 ； Timoshenko樑

並列摘要

In the industry, the damage detection of structures is an important research subject. To this end, a proper method for the vibration signal processing is indispensable. The Hilbert-Huang Transform (HHT), which has been successfully applied to many different fields in the last ten years, may provide a promising method for this purpose. The purpose of this research is to detect the crack on beams by HHT of transient flexural waves. First of all, the basic method named “Empirical Mode Decomposition” of HHT was introduced. Its basis of expansion is adaptive, so that it can produce physically meaningful representations of data from nonlinear and non-stationary processes. And then the difference of Bernoulli-Euler theory and Timoshenko theory associated with flexural waves were then discussed. It will be found that the flexural waves are dispersive by considering the wave velocity. Besides, the beams of Aluminum, Brass and Stainless Steel were considered in the experiments. The flexural waves were made by the impact force on beams. Applying the HHT on the measured acceleration data, the Hilbert spectrum can be obtained. From the figure the ridges represented the reflected waves from the boundary and the crack. By estimating the wave arrival time, the wave velocity and the crack location can be determined. The mean values of absolute relative error are all less than 2.5%. In addition, the characteristics on Hilbert spectrum of the damage size were also studied. This study may contribute to the damage size estimation in the near future.

並列關鍵字

crack detection ； Hilbert-Huang Transform ； Empirical Mode Decomposition ； flexural wave ； dispersive wave ； Timoshenko beam

參考文獻

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