Application of Non-stationary Time Series Data to Environmental Engineering Problems - from Physically based Gambler's ruin (GR) Model to Time-Frequency Analysis (TFA)
Date Issued
2016
Date
2016
Author(s)
Ye, Ting-Gu
Abstract
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.
Subjects
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
Type
thesis
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