研究生: 郭裕農
論文名稱: 時頻分析應用於高雄港潮位資料之研究
論文名稱(外文):Application of time-frequency analysis to the tidal data of Kaohsiung port
指導教授: 謝志敏
學位類別: 碩士
校院名稱: 國立高雄海洋科技大學
系所名稱: 航海科技研究所
中文摘要
本研究利用多種時頻分析法分析高雄港之潮位資料與颱風暴潮資料。使用方法包括傅立葉轉換、短時傅立葉轉換 (Short Time Fourier Transform, STFT)、摩雷特小波轉換 (Morlet Wavelet Transform)、強化的摩雷特小波轉換(Enhanced Morlet Transform)及希爾伯特-黃轉換 (Hilbert-Huang Transform, HHT)。分析案例包括:(1)無颱風期間的潮位資料 (2010年1月1日~1月31日)、(2) 2006 珍珠 (Chanchu) 颱風、(3) 2009 蓮花 (Linfa) 颱風,以及(4) 2009 莫拉克 (Morakot) 颱風期間高雄港測站的水位資料。由案例分析結果的比較,認定HHT具有最佳的時頻解析度,可供分析高雄港潮位和暴潮資訊。為了避免混模 (mode mixing) 的現象,本研究進一步採用總體經驗模態分解法 (Ensemble Empirical Mode Decomposition, EEMD) 拆解訊號,求得準確的內建模態函數(Intrinsic Mode Functions, IMF)。探討高雄港颱風暴潮的時間和頻率的分佈特性。根據分析所得的暴潮能量分佈,可以正確求得最大暴潮發生的時間;同時由IMF 1的變化也可以推算颱風暴潮對高雄港影響的時間。本研究同時比較上述多種時頻分析方法處理同一筆水位資料所得結果的異同,比較其優缺點以供後續研究採用。
關鍵詞:希爾伯特-黃轉換、時頻分析、總體經驗模態分解法; 內建模態函數; 潮位
Abstract
The time-frequency analysis is employed to analyze characteristics of tidal elevation at Kaohsiung port in this study. Fourier Transform, Short Time Fourier Transform (STFT), Morlet Wavelet Transform, Enhanced Morlet Transform, and Hilbert-Huang Transform (HHT) are utilized to perform the time-frequency analysis. Four cases including the tidal elevation at Kaohsiung port from 2010/1/1 to 2010/1/31, the Chanchu typhoon in 2006, the Linf typhoon in 2009, and the Morakot typhoon in 2009 are investigated. Due to the excellent time-frequency resolution of HHT, it is chosen to simulate the performance of frequency modulation interference suppression. It is based on the empirical mode decomposition (EMD) which generates a group of intrinsic mode functions (IMF). The Ensemble Empirical Mode Decomposition (EEMD) approach consists of sifting an ensemble of white noise-added signal and treats the mean as the final true result, so it prevents “mode mixing”. The Ensemble EMD (EEMD) is adopted to decompose the tidal elevation data to derive the intrinsic mod functions (IMF). This study also adopts HHT to study the phenomena of tidal elevation and storm surge, which are based on the observed tidal data. The characteristics of space and frequency distributions of these two phenomena can be revealed by the Hilbert spectrum. Therefore, according to Hilbert spectrum distribution of surge, it can acquire accurately the moment of inception of max surge. Meanwhile, it can predict the duration of influence of a storm surge on Kaohsiung port from the variation of the IMF 1. In addition, the study compares the difference between results given by Fourier Transform, Short Time Fourier Transform, Morlet Wavelet Transform, Enhanced Morlet Transform, and Hilbert-Huang Transform. Moreover, the study provides the advantages and disadvantages of those approaches as a reference for researches.
Key words: Hilbert-Huang Transform (HHT), Time-Frequency Analysis, Ensemble Empirical Mode Decomposition (EEMD), Intrinsic Mode functions (IMF), tidal elevation
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