基於整體經驗模式分解的集群分析

Abstract

總體經驗模態分解法是一個分析訊號的方法，利用其獨特的分解方式將一個訊號分解成一組本質模態函數。然而，這個方法有多重模態函數的問題，也就是同一頻率的訊號被分解成兩個本質模態函數。 將這兩個或以上函數疊加成一個單一模態的訊號來解決此問題，但是目前沒有一個一般性的準則以合併這些多重模態函數。本論文利用分群分析的方法提供一套準則以合併具有多重模態問題的本質模態函數。利用此分群方法合併所得的一組被分群的本質模態函數更為扼要且較具有實際上的物理意義。本論文所提供的方法被運用在兩個模擬的訊號、一個風力渦輪機所產生的聲音訊號以及一個由在臺灣草嶺地區一個觀測站所記錄到的地震訊號。特別的是，該地震訊號同時記錄主要的地震訊號與山崩所造成的震動訊號。這些運用的結果皆表示本論文提供的方法可以針對多重模態函數的問題提供一個決定性的改善，並且以樹狀圖的方式描述訊號的特徵。

Ensemble Empirical Mode Decomposition (EEMD) is an adaptive time-frequency data analysis method. Time series or signals can be decomposed into a collection of intrinsic mode functions (IMFs). Nevertheless, there appears a multi-mode problem where signals with a similar time scale are decomposed into different IMFs. A possible solution to this problem is to combine the multi-modes into a proper single mode, but there is no general rule on how to combine IMFs in the literature. In this paper, we propose to modify EEMD algorithm using the statistical clustering analysis and to provide a framework to combine the IMFs into a condensed set of clustered intrinsic mode functions (CIMFs). The method is applied to two artificially synthesized signals, wind turbine signal at Chunan Miaoli, and a seismic signal during the earthquake at Chi-Chi in 1999. Especially, this seismic signal contains not only the main seismic information but also the seismic motion from a landslide in Tsaoling area. The present method can separate the two signal from different sources correctly, and these applications of other examples demonstrate that, the present method offers great improvement over EEMD for extracting useful information.