非穩態時間序列資料在環境工程問題中的應用-以賭徒機率模型與時間頻率分析為例

Application of Non-stationary Time Series Data to Environmental Engineering Problems - from Physically based Gambler's ruin (GR) Model to Time-Frequency Analysis (TFA)

葉庭谷(Ting-Gu Ye)

指導教授 ： 蔡宛珊

國立臺灣大學/工學院/土木工程學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201603193

摘要

第一部分:非穩態機率賭徒漠型在泥沙濃度風險分析之應用
本論文利用序率方法模擬均一粒徑的泥沙顆粒在流體中之交換運動過程: 利用賭徒問題(Gambler’s ruin model) 序率模型估算不同流況的條件下，水中顆粒數達到水質標準中最大容砂量的機率，不同於前人，本論文利用蒙地卡羅模擬(Monte Carlo Simulation)建立賭徒問題(Gambler’s ruin model)的數值模型，該模型解決了理論模型無法考慮機率為非穩態的問題，並且可以計算模式中當水質達到最大含砂量時所需的步輻，進而推估所需的時間。為了比較數值及理論模型的差異，本論文利用台灣石門水庫霞雲站的資料作為示範案例，對每日庫區的水質濁度做有效的風險評估(Risk Analysis)，以利附近淨水廠水質處利作業控管時參考，其中考量到計算泥沙運動機率時資料隱含很大的不確定性，故結合不確定性分析(Uncertainty Analysis)以考慮日水位的不確定性對有效風險的影響變化。

第二部分:時頻分析在登革熱及水文時間序列分析上之應用
近年來全球暖化造成全球的氣候異常也誘發許多複合型的災害，近幾年登革熱在台灣南部地區造成了許多的危害，在氣候條件的改變下登革熱的發生頻率有越來越高的趨勢，地域性也有漸漸向北的趨勢，其中有許多研究單位提出登革熱的散佈可能與降雨、潮位、氣溫…等水文氣像因素的改變有極為密切的關連性。本論文希望利用近年來被廣泛利用在各大領域的幾個時頻分析工具(短時距傅立葉轉換、小波轉換、希爾伯特-黃轉換)，來對長時間的水文氣象時序資料進行時頻分析，並且拆解出不同尺度的事件分析極端事件發生的頻率變化，最後將結果與登革熱病發的時序資料進行頻率分析，比較這些水文氣象因子的頻率變化是否影響登革熱疫情之散佈。

關鍵字

泥砂運動 ； 賭徒問題 ； 不確定分析 ； 蒙地卡羅模擬 ； 水文資料時序分析 ； 登革熱 ； 時頻分析 ； 短時距傅立葉轉換 ； 小波轉換 ； 希爾伯特-黃轉換 ； 非穩態時間序列

並列摘要

Part I: Water Quality Risk Analysis
The Gambler’s ruin model has been employed to estimate the probability of reaching the designated sediment capacity such as the pre-established water quality standard or maximum sediment carrying capacity in reservoirs with different flow conditions. However, this theoretical model has a stationary probability assumption used to reduce mathematical complexity. In this study, we develop a non-stationary Gambler’s ruin model by using the Monte Carlo simulation method. Finally we use the daily water level data of the Xia Yun hydrologic station to predict the effective risk of reaching the maximum capacity of the water treatment plant in the Shihmen Reservoir in 2008. Compared with previous work, this non-stationary model could obtain more accurate probability, which can be proved using measured daily concentration data of the Shihmen Reservoir.

Part II: Time Frequency Analysis
Extreme events occur more and more frequently due to climate change. Recently the dengue fever is a pressing issue of southern Taiwan, and the dengue fever might have characteristic temporal scales that can be further identified. Some researchers hypothesized that the dengue fever events might have linkage with climate change. In this study we propose to use the time-frequency analysis to observe time series data of the dengue fever, and hydrologic and meteorological variables. In addition, we also compare and discuss the analysis results from three time-frequency methods, the Hilbert Huang transform (HHT), the Wavelet transform (WT) and the short time Fourier transform (SFFT). A more suitable time-frequency analysis method will be identified and selected to further analyze relevant time series data pertinent to the aforementioned issue. The most influential time scales of hydrologic and meteorological variables associated with dengue fever can be identified. Finally the linkage between hydrologic/meteorological factors and the number of dengue fever incidences can be established.

並列關鍵字

the Monte Carlo simulation ； discrete-time Markov chain ； Gambler’s ruin problem ； reservoir risk analysis ； climate change ； dengue fever ； time-frequency analysis ； Hilbert Huang Transform ； Wavelet Transform ； Short Time Fourier Transform ； Non-stationary time series data

參考文獻

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