應用希爾伯特 – 黃轉換發展即時橋梁健康監測

Abstract

臺灣河川陡峭、水流湍急，在季風及颱風來臨期間，西南氣流帶來豐沛的降雨量，常在短時間內帶以瞬時暴雨情形，又臺灣地質穩定性差，橋梁設計上還有天然、人為災害等因素需要考慮，而橋梁受沖刷卻是一個相當複雜的動力行為，包含水深、水流的角度和強度、橋墩和橋台的形狀和寬度、沉積物的物質屬性等因素沖刷對於橋梁、堤防等結構物基礎下基座造成的沖刷危害十分嚴重。 希爾伯特轉換(Hilbert-HuangTransform, HHT)法在訊號分析上具有對非線性、非週期性及非穩態性訊號上的可適性，又具有時變性(Time variable)之特點，由於橋梁行為在受到沖刷影響時，結構物-土壤-水流的互制效應為非線性行為，隨著河床掏刷過程，其亦非穩態性行為，利用整體經驗模態分解法(Ensemble Empirical Mode Decomposition, EEMD)對訊號作分解，以得到故有模態函數(Intrinsic Mode Functions, IMF)，然後藉由IMF之間的正交性的正交指數(Index of Orthogonality)來將IMF分作為控制橋梁頻率變化之主頻因子(Principle Frequency Factor, Pf)以及控制橋梁在做剛體運動部分之主動因子(Principle Rigid Body Motion Factor, Pr)。爾後先將IMF先計算其各自的瞬時頻率(Instantaneous Frequency, IF)並與能量加權得到加權瞬時頻率(Weight Instantaneous Frequency, wIF)，及後藉由Pf以及Pr來作為平均加權瞬時頻率(Average Weight Instantaneous Frequency, AwIF)的依據。Pf以及Pr的AwIF與之所有的IMF所做出的AwIF相除比較得到安全係數(UnSafety Index, UI)，由安全係數可以看出結構物行為上的改變，並提供預警。 藉由單樁沖刷實驗，將橋樁沖垮可以得到橋樁被沖垮時的行為紀錄，由紀錄的分析來看，UI在橋樁明顯傾斜前，UI漸漸與原來保持固定範圍內的值偏離許多，一旦偏離超過太多時，則可以預先發出警訊給予使用者警告，以此得以在危險發出之前提供足夠的時間進行橋梁的撤離以及封閉或修繕。

In Taiwan, rivers are steep, fast-flowing. During the monsoon and typhoon, southwesterly airstream brings abundant rainfall, often in a short time with the situation in the instantaneous rain. And Taiwan has poor geologic stability. There are natural disaster and man-made factors to consider, but it is a bridge subject to erosion rather complex dynamical behavior, including water depth, flow angle and intensity, the shape and the width of piers and abutments , the material properties of sediment erosion and other factors for bridges, embankments and other structural base erosion caused quite serious harm. Hilbert-Huang Transform (HHT) method has the adaptation of nonlinear signal analysis, non-cyclical and non-steady-state signal, but also has a the characteristics of time-varying. As a bridge is affected by erosion, the structure-soil-water flow interaction effect is the nonlinear behavior. With the process of the riverbed scouring, it’s not a steady-state behavior. Using Ensemble Empirical Mode Decomposition (EEMD) decompose the signals to obtain Intrinsic Mode Functions (IMF). And then by using the orthogonal index of IMF to divide the IMF into Principle Frequency Factor (P_f), and Principle Rigid Body Motion Factor (P_r). Later, calculates IMF its own instantaneous frequency (IF) first and then have it weighted with the energy to get Weight Instantaneous Frequency (wIF). And secondly, P_f and P_r are as the Average Weight Instantaneous Frequency (AwIF) basis. Dividing P_f and P_r of AwIF with AwIF contributed by all of the IMF, and compare them to get the UnSafety Index (UI). The behaviors of structure changes can be seen by the UnSafety Index, therefore, UI can provide early warning. By pile erosion experiments, washing away the pile of bridge and the behavior of the washed away pile can be recorded. According to the analysis of record, before pile apparently tilt, UI gradually deviate from the original value within a fixed range a lot. Once deviating too much, then it can give users advanced warning alerts to provide sufficient time to evacuate, seal the bridge or fix it.