Application of Continuous-time Markov Chain and Gambler’s ruin Problem to Sediment Transport Modeling
Date Issued
2012
Date
2012
Author(s)
Lai, Kung-Chung
Abstract
In this study, the interaction process of mixed-size sediment particles under steady flow is described using two different stochastic approaches: the continuous-time Markov process and Gambler’s ruin problem. The continuous behavior of particle movement among the bed material, bedload and suspended load layer is modeled using a continuous-time Markov process. Therefore, the probability of particles staying in each layer is acquired, which can be used to quantify the number of particles and hence the bedload and suspended load transport rate. In addition, particle size distribution is taken into consideration. Then, the proposed model is verified against the experimental data with both bedload and suspended load particles. Modeling results of bedload and suspended load transport rate show a reasonable agreement with measurement.
On the other hand, another approach: Gambler’s ruin problem is adapted to model sediment particle interaction between the bed material and water column. With several transitions between bed material and water column, the probability starting from a given number of sediment particles to the maximum number of sediment particles in the water column and the mean time spent can be acquired. As a result, we attempt using Gambler’s ruin problem to simulate the effective risk of reaching to the limitation of the water quality standard that can be handled by the water treatment plant. Besides, we have incorporated the uncertainty analysis into Gambler’s ruin problem to quantify the variability of the effective risk in Shihmen reservoir basin. Model results including the expected value and confidence interval of effective risk are presented in the study.
Subjects
sediment particle interaction
stochastic model
uncertainty analysis
continuous-time Markov process
Gambler’s ruin problem
Type
thesis
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