應用HHT於軌道結構分析之研究

Rail Structure Analysis by Hilbert Huang Transform

曾志豪(Zhi-Hao Zeng)

指導教授 ： 張達德

中原大學/工學院/土木工程學系/碩士(2006年)

https://doi.org/10.6840/cycu200600450

摘要

軌道運輸系統由於其具方便、快捷及準時等特性，在現今儼然已成為人民生活上不可或缺的一部份。由於列車高速的行駛，突顯了軌道結構系統安全維護的重要性。軌道結構系統安全檢測之目的，即為確保列車於行駛過程中安全性與舒適性，並做到防災、避災之目的。
因此提出一套振動模態分析新方法-HHT﹙Hilbert Huang Transform﹚，此方法係結合尖端高科技振動檢測儀器，進行非破壞振動檢測試驗。
本研究主要目的乃是期望在進行振動解析之前，藉由實驗室模擬試驗及現地動態車載試驗，搭配本研究所採用的HHT振動模態分析法、與傳統快速傅立葉分析法，對於鋼軌各方向的頻率做初步探討。得知該頻率範圍，後續在現地試驗規劃中以道碴整碴不齊或路基掏空以致軌道不平順模擬測試為主題，嘗試找出加速度計佈設的位置及配置距離以達到有效的量測。所獲得的結果是否能以振動歷時訊號加以損傷定位，驗證軌道振動訊號分析之可行性與適用性。
根據研究結果驗證鋼軌垂直向與水平向的頻率值與文獻所界定的範圍相同，而軸向因受內部應力所影響故主頻率範圍較大約1200~1600 Hz，且由現地試驗得知，加速度計於鋼軌上量測有效的佈設範圍前後間隔約8m，就檢測經濟效益來說是不佳的，而佈設於機車頭上方量測可以有效率的量測。由該試驗驗證相較於傳統的快速傅立葉分析，其所得到的頻率乃只是與時間無關之平均自然頻率，因此無法有效得知軌道結構真實的損傷位置，然而，HHT可獲得隨時間變化之即時頻率與能量刻度，可有效的推算出軌道結構損傷位置。由此可知HHT振動模態分析法可獲得較佳的解析。

關鍵字

經驗模態分解法 ； 快速傅立葉分析 ； 希爾伯特-黃轉換

並列摘要

The transportation system of the track characteristic is convenient, swift and on time. Today it has already become a part of indispensable in people’s life. The high speed train going emphasizes the importance of the structure system maintenance.
The purposes of measuring the structure system of the rail are the train security guarantee, comfortableness in the course of going, disaster prevention and calamities avoidance. Accordingly, the new method which is vibration mode analysis - HHT (Hilbert Huang Transform) is proposed. This method uses the Hi-Tech vibration detecting instrument and does nondestructive inspection test.
The main purpose of this research is to expect the preliminary discussion on the frequency of rail every direction before analyzing vibration by the test of the laboratory simulation and in-situ dynamic train test with the HHT vibration mode analysis and traditional Fast Fourier Transform analysis applied in this study. With the range of frequency, next step is to focus on in-situ test plan which is trying to find out the position and distance of accelerometer installation to reach effective measures by the sub ballast arrangement irregularity or hollow of sub ballast which causes the rail non-smoothly. If the outcome of this study can confirm the damage position with vibration signal and prove the feasibility and suitability of the track vibration analysis will be discussed.
According to the result of study proves that the rail in the vertical direction and horizontal direction have the same frequency range definition with the references, and the main frequency range is influence on inside stress of axial direction probably 1200~1600 Hz, and by in-situ dynamic train test learn accelerometer at rail effective on quantity examine laying ranging interval between 8 m, so it is not good for the economic benefits, setting up the accelerometer on the top of the locomotive can measures effectively.

As the result of study it proves the relatively analysis of the traditional Fast Fourier Transform, Average natural frequency that the frequency received has nothing to do with time, It can not find the damage position with vibration signal effectively,However, Instantaneous frequency and energy scale could be obtained as the variation of time by HHT, by this way you can calculate the damaging position in the rail structure. Therefore HHT vibration mode analysis method can get the better analysis.

並列關鍵字

Empirical Mode Decomposition ； Fast Fourier Transform Analysis ； Hilbert-Huang Transform

參考文獻

N.E. Huang , 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

Nonstationary Time Series Analysis " ,Proc. R. Soc. Lond. A 454, pp. 903-995, 1998.

N.E. Huang , M.C. Wu, S.R. Long, S.S.P. Shen, W. Qu, P. Gloersen & K.L. Fan, "A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis " ,Proc. R. Soc. Lond. A 4549, pp. 2317-2345, 2003.

R. Bracewell, "The Fourier transform and its application", New York:McGraw-Hill", 1965.

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