以序率模式探討泥砂運動機制

Application of Continuous-time Markov Chain and Gambler’s ruin Problem to Sediment Transport Modeling

賴冠中(Kung-Chung Lai)

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(2012年)

https://doi.org/10.6342/NTU.2012.00422

摘要

於天然河川泥砂粒徑組成不均及泥砂於水體中進行複雜交換運動過程，本研究將分別利用兩種不同序率方法模擬混合粒徑泥砂在穩定流中運動情形。方法一，考慮泥砂顆粒受遮蔽效應影響之輸砂率，建立連續時間馬可夫鍊序率模型，我們著重於描述泥砂在不同水流情況下，底床、推移層及懸浮層之交換過程；方法二，為賭徒問題序率模型在泥砂交換過程上的應用，此模型探討泥砂在不同水流及泥砂粒徑情況下可到達機率，進而採用石門水庫為例，做為模型應用並結合不確定分析方法加以討論，綜合上述得知，我們能由序率方法了解完整泥砂連續交換運動過程。

關鍵字

泥砂交換過程 ； 序率模型 ； 不確定分析 ； 連續時間馬可夫鍊 ； 賭徒問題

並列摘要

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.

並列關鍵字

sediment particle interaction ； stochastic model ； uncertainty analysis ； continuous-time Markov process ； Gambler’s ruin problem

參考文獻

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