總體型經驗模態分解法的改善研究

A New Approach to Improve Ensemble Empirical Mode Decomposition Method

林俶寬(Chu-Kuan Lin) ； 許師瑜(Shih-Yu Hsu) ； 黃偉柏(Wei-Po Huang) ； 林炤圭(Jaw-Guei Lin)

《海洋工程學刊》 15卷2期 (2015/06) Pp. 85-99

https://doi.org/10.6266/JCOE.2015.1502.02

摘要

本文主要針對應用Wu and Huang（2008）發展的總體型經驗模態分解法（ensemble empirical mode decomposition, EEMD）進行海洋觀測波浪資料時之適切性進行探討並對建立總體樣本時所添加之白噪音雜訊方式提出改良建議。EEMD可以不需要像傳統EMD（empirical mode decomposition）方法中所訂定的停止篩選準則，而且IMF的個數可以藉由取樣點數預估，同時也可以解決EMD分析中會有的波動模態混合問題。在考量利用電腦程式語言產生白噪音雜訊時的隨機性，其所建立之總體樣本是否在最後求平均值時是否能完全消除添加之雜訊有必要做進步的確認，以避免殘存額外的訊號影響分析。本文首先針對EEMD中所加入的白噪音雜訊方式進行討論並發現即便總體樣本數達到10,000組也仍有殘餘訊號，無法完全被消除，也因此造成有額外的波動成分摻入到原始訊號中，而且雜訊部分亦無法完全滿足高斯分布。本研究改以要求每一個時間點上的總體雜訊必須滿足高斯分布的方式建立指定組數的雜訊值，再以隨機挑選方式建置雜訊時間序列並附加到時序訊號中，而後進行篩選處理。此一方法可以讓總體附加雜訊在每一個取樣點上均滿足高斯分布的特性，也確認雜訊可以在改良EEMD的處理中完全去除。此外，也可以縮減建置總體樣本時所需要的樣本組數至50組，以節省分析時間。

關鍵字

經驗模態分解法 ； 時間序列 ； 波浪觀測 ； 白噪音雜訊

並列摘要

The suitability of ensemble empirical mode decomposition method (EEMD) by Wu and Huang (2008) on ocean wave analysis was evaluated in this paper and some suggestions about the establishment of the ensemble and related added noises were made. Unlike the conventional empirical mode decomposition method (EMD), the EEMD doesn't need the stopping criteria check of sifting, and the number of intrinsic mode function can be estimated, and also it solved the mode mixing problem which was found in EMD analysis. Considering the establishment of ensemble itself has highly randomness, this paper firstly focused on the added noises in EEMD process and found that even though with huge number of trials in the ensemble, the accumulated added white noises cannot satisfy Gaussian distribution with zero mean, which means that there are still some extra signals residue in the results. An adjusted EEMD was then promoted to solve such problem. A set of noises which satisfies the Gaussian distribution with zero mean was firstly created and applied to each sample point. Each added noise set in the ensemble was generated by randomly pick up a value without repeated from the noise data set at each sample point to form the time series. In this way, the noises at each sample point in the ensemble can definitely be averaged out from the original signal to ensure the final results of adjusted EEMD sifting process are components of original signal, and also the number of trial of the ensemble can be limited to 50 sets.

並列關鍵字

ensemble empirical mode decomposition ； time series ； water waves ； white noise