以經驗模態分解與時依性本質相關係數應用於非穩態與非線性水文、環境、疾病時間序列之研究

Abstract

在估計兩變數時間序列之相關性時，一般使用傳統的皮爾森相關係數分析。然而，許多的時間序列為非穩態、非線性、多尺度且含有噪音之信號，這樣的特性使皮爾森相關係數分析產生了偏估。如欲對具有上述特性的信號做相關性分析，時頻分析是一個十分有用的工具，此法能夠透過時域與頻域的能量分佈，抓取信號的特徵尺度，再對顯著且具有物理意義的特徵尺度做多尺度相關性分析。雖然時頻分析能夠抓取頻域特徵，不過在傳統的時頻分析方法(例如:短時距傅立葉分析、小波分析)中，皆是基於線性假設，仍會造成相關性分析的偏估。在本研究中，引入了希伯特黃轉換中的經驗模態分解法，萃取訊號的非線性特徵。因為經驗模態分解法在多變量訊號的分解上，有濾波器無法統一的問題，本研究更引入了多變量加噪經驗模態分解法，增加多尺度相關性分析的精確性。在多尺度相關性分析的部分，本研究使用了時依性本質相關係數法與時依性本質交錯相關係數法，分別探討相關係數與遲滯效應隨時間的變化。 本研究將以上的時頻分析與相關係數估計法應用於空氣汙染與疾病議題上。在空氣汙染的部分，係關注高雄地區橋頭、楠梓和前金三個測站的〖PM〗_2.5時間序列與相關水文大氣時間序列在不同尺度的相關性。本研究發現〖PM〗_2.5時間序列在半日、一日與年尺度的能量上具有顯著性，故以這三個尺度進行相關性分析。在年尺度上，〖PM〗_2.5與溫度、相對濕度、降雨間皆觀察到強烈的負相關。在半日及一日尺度上，〖PM〗_2.5與溫度、相對濕度間皆觀察到相關係數會呈現或強或弱的季節性的變換。在多變量加噪經驗模態分解應用於結合風速、風向資料的聯合拆解上，〖PM〗_2.5被發現與年尺度的冬季季風與日尺度的東風有密切的關係。在此部分的最後，本研究引入非線性量化分析，證實經驗模態分解法的確能分離出時間序列的非線性特徵。在疾病議題的部分，係關注高雄地區登革熱時間序列與相關水文大氣時間序列在大尺度的相關性與遲滯效應變化。在登革熱病例時間序列的尺度分析部分，一年與四年尺度具有顯著性。在一年尺度上，時依性本質交錯相關係數法揭露了登革熱病例與降雨、相對溼度、溫度時間序列的遲滯效應會隨時間產生變化，遲滯的時間會在登革熱爆發期和平常時期有所不同。在四年的尺度上，時依性本質相關係數法揭露了聖嬰現象與登革熱爆發期的相關性。 從本研究中可以發現，在面對非線性非穩態解含有多尺度的多變量時間序列，如不同變量的資料解析度相同，則多變量加噪經驗模態分解相較於單變量經驗模態分解及連續小波分析更為適用。

Time frequency analysis is a powerful tool to investigate the characteristic time scale and energy distribution of a signal. However, assumptions of the linearity and non-stationary character of the signal limit the estimation of any correlation between two variables using traditional time-frequency techniques (such as short-time Fourier transform, wavelet transform and others.). Thus, a method of noise-assisted multivariate empirical mode decomposition (NAMEMD)-based spectral analysis is introduced. A time-dependent intrinsic correlation (TDIC) algorithm is also introduced to gain some insight into variation of any correlation over time. A time-dependent intrinsic cross-correlation (TDICC) algorithm is introduced to elucidate the time-varying lag effect. The above algorithms are applied to data on air pollution and dengue fever. In the application to the air pollution problem, the association among 〖PM〗_2.5 and hydro-meteorological variables are characterized at three monitoring stations in Kaohsiung. The annual, diurnal and semi-diurnal scale are identified to be significant. The correlation obtained from filtered signal is found to be physically more representative than the Pearson correlation. The seasonal switchover of correlation is observed by time dependent intrinsic correlation analysis in the association among 〖PM〗_2.5 and temperature and relative humidity at diurnal and semi-diurnal scales. It is identified that the concentration of 〖PM〗_2.5 is related to the land breeze at diurnal scale, which corresponds to the monsoon during the winter at annual scale. A novel measurement of nonlinearity is introduced to quantify the difference between empirical mode decomposition (EMD)-based methods and Fourier-based methods. In the application of dengue fever issue, the long-term association among dengue fever incidences and hydro-meteorological variables are characterized. The inter-annual (4-year) and annual scale are identified to be significant in dengue fever incidences. The fluctuation of lag effect is observed by TDICC among dengue fever incidences, precipitation, relative humidity and temperature at annual scale, indicating the diverse mechanism during the epidemic periods and normal time. It is confirmed that the outbreak of dengue fever is associated with the El Niño-Southern Oscillation (ENSO) events by TDIC. It is revealed in this thesis that the NAMEMD algorithm to be the best filtering technique while dealing with complicated multivariate data compared to EMD and continuous wavelet transform (CWT) when the multiple data resolution is identical to each other.