時頻分析與地球科學研討會-活動紀實

張貼日期：Oct 25, 2010 9:12:11 PM

時頻分析與地球科學研討會-活動紀實

2008/4/1 Posted by AnCADSupport under Visual Signal

本次逸奇科技與中研院地球所合作舉辦「時頻分析與地球科學研討會」，邀請到多位學者，包括發明HHT (Hilbert-Huang Transform)的黃鍔院士，為大家帶來相關研究成果的發表，我們也很高興的看到超過150名的參加者前來共襄盛舉。相關照片及教材下載聯結如下:

活動議程 (依演講順序排列):

1. 適應性資料分析之應用與推廣 投影片下載

黃 鍔博士/中央大學數據分析方法研究中心

Traditionally, we made the critical linear and stationary assumption even before

we look at any data. But the world we live in is neither stationary nor linear.

Facing with such reality, what should we look for in the data? The existing

methods of probability theory and spectral analysis are certainly inadequate, for

they are all based on the stationary and linear assumptions. For example,

spectral analysis is synonymous with the Fourier based analysis. As Fourier

spectrum can only give meaningful interpretation to linear and stationary

process, its application to data from nonlinear and nonstationary processes is

problematical. To break away from this limitation, we should let data speak

for themselves. We should develop adaptive data analysis techniques.

A new method, Hilbert-Huang Transform (HHT), for analyzing nonlinear and

nonstationary data has been developed. The key part of HHT is the Empirical

Mode Decomposition method with which any complicated data set can be

decomposed into a finite and often small number of Intrinsic Mode Functions

(IMF). An IMF is defined as any function having the same numbers of

zero-crossing and extrema, and also having symmetric envelopes defined by the

local maxima and minima respectively. The IMF also admits well-behaved

Hilbert transform. This decomposition method is adaptive, and, therefore,

highly efficient. Since the decomposition is based on the local characteristic

time scale of the data, it is applicable to nonlinear and nonstationary processes.

With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous

frequencies as functions of time that give sharp identifications of imbedded

structures. The final presentation of the results is an energy-frequency-time

distribution, designated as the Hilbert Spectrum. Classical nonlinear system

models are used to illustrate the roles played by the nonlinear and nonstationary

effects in the energy-frequency-time distribution. Other applications of HHT

will also be presented.

2. 從溫度記錄看台北的暖化現象 投影片下載

汪中和博士/中央研究院地球所

利用Visual Signal 分析工具，探討台北百年來溫度紀錄的特徵，一方面可

以觀察溫室效應帶來的全球性暖化現象，另一方面藉由低頻訊號的分離，

區分地區性的影響因素，可對環境變遷的研究，帶來更多的啟發。

3. 時頻分析用於地下水位異常變化及地震前兆的預測 投影片下載

王逸民博士/逸奇科技

透過頻率隨時間的變化我們可以看到豐富的訊息，不論是地下含水層的補

助及滲出，或是波峰的動態移動，都可能是地震的前兆。這次的研究中指

出了固體振動的頻率分佈，而且先前的地下水水位變化所紀錄的地震記錄

信號， 具有很高的取樣率(sampling rate=1Hz)。利用時頻分析，我們可

以得知含水層有一個30 分鐘的共振頻率。如果能提早識別這種共振，或

許可以作為未來地震前兆的預測。

4. 分析海潮負載對重力數據之影響實例應用

彭淼祥博士/工研院量測中心長度研究室

潮汐時頻分析，海潮負載計算，海潮負載對重力變化之影響

5. 高辨識度時頻轉換及波模態析離的最新發展 投影片下載

鄭育能博士/國立成功大學 航空太空工程學系

以快速方法求得疊代式高斯平滑法的結果,以分離出平滑和週期性部

份.其中平滑部份含有部份極低頻的週期波.對週期性部份以Fourier

cosine/sine spectrum generator 產生其頻譜.因為time domain 之Gaussian

window 對應到spectral domain 之對應Gaussian window,故可對頻譜直接取

Gaussian window,其inverse Fourier transform 即為wavelet coefficient 或

spectrogram coefficient.所得到的wavelet coefficient plot 和spectrogram plot

之visibility 優於原來的方法.由於可以找到subjet to uncertainty principle 之

pseudo-one-to-one-onto mapping between Fourier spectrum ＋ original

data and spectrogram,故可以用疊代法找出(t,f)點的mode information.所用

的疊代法對於mode m 與mode 之間有明顯spectral gap 之複合波可以分離

出各個mode.

6. 時頻分析應用在異常波浪的分析 投影片下載

董東璟博士/國立台灣海洋大學 海洋環境資訊系

(1) use Visual Signal 時頻分析 on freak wave data analysis

(2) use Visual Signal EMD on long-period Tide data analysis

Visual Signal 軟體試用下載 - 進行時頻分析訊號處理，毋需撰寫程式

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