跳到主要內容

臺灣博碩士論文加值系統

(18.205.192.201) 您好!臺灣時間:2021/08/05 08:55
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:洪毓茹
研究生(外文):Yu-Ju Hung
論文名稱:以排隊理論及隨機顆粒軌跡模型模擬隨機泥砂傳輸下之泥沙傳輸率及濃度變化
論文名稱(外文):Application of Queueing Theory and Stochastic Particle Tracking Model to Simulating Stochastic Sediment Transport: Concentrations and Transport Rates
指導教授:蔡宛珊蔡宛珊引用關係
口試委員:吳富春余化龍游景雲
口試日期:2015-07-06
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:英文
論文頁數:111
中文關鍵詞:排隊理論隨機泥砂進入隨機泥沙傳輸序率模式顆粒軌跡模型顆粒隨機被帶起卜松過程二項分布
外文關鍵詞:queueing theorysediment transportrandom inputSD-PTMstochastic methodparticle tracking model
相關次數:
  • 被引用被引用:0
  • 點閱點閱:127
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
泥砂傳輸在傳統上通常使用定律模型進模擬。然而其間歇性(intermittent)與其隨機(stochastic)的特性使泥砂傳輸更為適合以離散隨機的方法進行描述。本研究運用排隊理論(queueing theory) 以離散隨機的方式設計出一隨機模型的框架,此框架可以用來模擬泥砂顆粒在水中隨機的進入控制體積的行為。泥砂顆粒、控制體積、泥砂傳輸的機制(包含懸浮、沉澱以及從底床被帶起的機制)分別對應於排隊理論中的顧客、商店以及服務。在本研究中主要以隨機擴散粒子追蹤模型(SD-PTM)以及底床顆粒被帶起為主要的泥砂傳輸機制。排隊理論最大的特點在於可以模擬顧客數量及到顧客達時間的隨機性,將此特性運用到泥砂傳輸,就可以進行泥砂顆粒在水中隨機的進入控制體積的行為模擬,其中泥砂顆粒的隨機進入包含泥砂隨機的到達以及每次到達含有隨機的泥砂顆粒數量。本研究以卜松過程(Poisson process)和二項分布(binominal distribution)分別模擬泥砂的隨機到達(random arrivals)以及每次到達的隨機泥砂數量(random magnitude)。
本研究含有三個不同的泥砂進入機制的模擬,分別是泥砂進入控制體積的時間是固定的,但是每次的量是隨機的(random magnitude, RM)、泥砂每次進入控制體積的量為固定的,但是進入控制體積的時間是隨機的(random arrivals, RA)以及泥砂進入控制體積的時間不固定而且每次的量也是隨機的(random-sized batch arrivals)。模擬結果以系綜統計(ensemble statistics)進行分析,統計的系綜包含泥砂濃度、泥沙傳輸速率的系綜平均(ensemble means)和系綜方差(ensemble variances)。再對三種不同的泥砂進入機制的模擬的結果進行比較,比較的結果顯示在相同的平均泥砂輸入速率下,不同於系綜平均,系綜方差的值可以反映出不同的泥砂進入機制。


Sediment transport is typically simulated using deterministic models. However, the intermittent and stochastic features of sediment transport make it suitable to be described by discrete random processes. This study attempts to apply queueing theory to develop a stochastic framework that could account for the random-sized batch arrivals of incoming sediment particles into receiving waters. Sediment particles, control volume, mechanics of sediment transport (such as mechanics of suspension, deposition and resuspension) are treated as the customers, service facility and server respectively in queueing theory. In the framework, the stochastic diffusion particle tracking model (SD-PTM) and resuspension of particles are included to simulate the random transport trajectories of suspended particles. The most distinguished characteristic of queueing theory is that customers come to the service facility in a random manner. In analogy to sediment transport, this characteristic is suitable to model the random-sized batch arrival process of sediment particles including the random occurrences and random magnitude of incoming sediment particles. The random occurrences of arrivals are simulated by Poisson process while the number of sediment particles in each arrival can be simulated by a binominal distribution. Simulations of random arrivals and random magnitude are proposed individually to compare with the random-sized batch arrival simulations. Simulation results are a probabilistic description for discrete sediment transport through ensemble statistics (i.e. ensemble means and ensemble variances) of sediment concentrations and transport rates. Results reveal the different mechanisms of incoming particles (RM, RA and BA) will result in differences in the ensemble variances of concentrations and transport rates under the same mean incoming rate of sediment particles.

CONTENTS
誌謝 iii
中文摘要 v
ABSTRACT vii
CONTENTS ix
LIST OF FIGURES xiii
LIST OF TABLES xvii
Chapter 1 Introduction 1
1.1 Motivation and Objective of the Study 5
1.2 Overview of the Thesis 5
Chapter 2 Literature Review 7
2.1 Queueing Theory 7
2.2 Brownian Motion 8
2.3 Stochastic Particle Tracking Model 9
2.4 Pickup Probability 11
2.5 Experimental Data 12
Chapter 3 Theoretical Framework 13
3.1 Application to Queueing Theory 13
3.1.1 Notation 15
3.2 Exponential Distribution 16
3.3 Continuous-Time BAMPS 17
3.3.1 Batch Markovian Arrival Processes (BMAP) 17
3.3.2 The Continuous-time BMAP 17
3.3.3 Poisson Process 19
3.3.4 Batch Poisson Process 20
Chapter 4 Random Magnitude (RM) Simulated by Binomial Distribution 21
4.1 Introduction 21
4.2 Assumptions 22
4.3 Procedure 22
4.4 Simulations 23
4.4.1 Case RM-1D 23
4.4.2 Case RM-2D (without resuspension) 39
4.4.3 Case RM-2D 48
Chapter 5 Random Arrivals (RA) Simulated by Poisson Process 63
5.1 Introduction 63
5.2 Assumptions 64
5.3 Procedure 64
5.4 Simulations 65
5.4.1 RA-2D 65
Chapter 6 Random-sized Batch Arrivals Simulated by Batch Poisson Process 77
6.2 Assumptions 78
6.4 Simulations (BA-2D) 79
6.4.1 Simulation Results 83
6.4.2 Model Validation 89
6.4.3 Comparison between BA -2D cases 90
6.4.4 Comparison of RM, RA, and BA 95
6.4.5 Summary 100
Chapter 7 Summary and Recommendations 103
7.1 Summary and Conclusion 103
7.2 Recommendation for Future Research 107
REFERENCE 109


[1]Dimou, K. N., & Adams,E. E. (1993). A random-walk, particle tracking model for well-mixed estuaries and coastal waters. Estuarine, Coastal and Shelf Science, 37(1), 99-110.
[2]Gorenflo, R., Mainardi, F., Moretti, D., & Paradisi, P. (2002). Time fractional diffusion: a discrete random walk approach. Nonlinear Dynamics, 29(1-4), 129-143.
[3]Ross, S. M. (2007). Introduction to probability models. Chapter 8. Academic press.
[4]Al Hanbali, A., & Boxma, O. (2010). Busy period analysis of the state dependent M/M/1/K queue. Operations Research Letters, 38(1), 1-6.
[5]Ancey, C., Davison, A. C., Böhm, T., Jodeau, M., & Frey, P. (2008). Entrainment and motion of coarse particles in a shallow water stream down a steep slope. Journal of Fluid Mechanics, 595, 83-114.
[6]Arnold, J. G., & Williams, J. R. (1988). HYDROLOGIC MODELING USING A SIMULATION LANGUAGE BASED ON QUEUEING THEORY1.
[7]Arunachalam, V., Gupta, V., & Dharmaraja, S. (2010). A fluid queue modulated by two independent birth-death processes. Computers & Mathematics with Applications, 60(8), 2433-2444.
[8]Batchelor, G. K. (1977). The effect of Brownian motion on the bulk stress in a suspension of spherical particles. Journal of Fluid Mechanics, 83(01), 97-117.
[9]Bridge, J. S. (1981). A discussion of Bagnold''s (1956) bedload transport theory in relation to recent developments in bedload modelling. Earth surface processes and landforms, 6(2), 187-190.
[10]Cordeiro, J. D., & Kharoufeh, J. P. (2011). Batch Markovian arrival processes (bmap). Wiley Encyclopedia of Operations Research and Management Science.
[11]Dimou, K., 1989. Simulation of estuary mixing using a 2-dimensional random walk model, MS thesis, MIT.
[12]Gorenflo, R., & Mainardi, F. (1998). Random walk models for space-fractional diffusion processes. Fractional Calculus and Applied Analysis, 1(2), 167-191.
[13]Malhotra, R., Mandjes, M. R., Scheinhardt, W. R. W., & Van den Berg, J. L. (2009). A feedback fluid queue with two congestion control thresholds. Mathematical methods of operations research, 70(1), 149-169.
[14]Malmon, D. V., Dunne, T., & Reneau, S. L. (2003). Stochastic theory of particle trajectories through alluvial valley floors. The Journal of geology, 111(5), 525-542.
[15]Mitra, D. (1988). Stochastic theory of a fluid model of producers and consumers coupled by a buffer. Advances in Applied Probability, 646-676.
[16]Naden, P. (1987). Modelling gravel‐bed topography from sediment transport. Earth Surface Processes and Landforms, 12(4), 353-367.
[17]Oh, J. (2011). Stochastic particle tracking modeling for sediment transport in open channel flows. State University of New York at Buffalo.
[18]Oh, J., & Tsai, C. W. (2010). A stochastic jump diffusion particle‐tracking model (SJD‐PTM) for sediment transport in open channel flows. Water Resources Research, 46(10).
[19]Oh, J., & Tsai, C. W. (2014). A stochastic multivariate framework for modeling the movement of discrete sediment particles in open channel flows.
[20]Oh, J., & Tsai, C. W. (2014). A stochastic particle based model for suspended particle movement in surface flows.
[21]Pope, S. B. (1994). Lagrangian PDF methods for turbulent flows. Annual review of fluid mechanics, 26(1), 23-63.
[22]Schumer, R., Meerschaert, M. M., & Baeumer, B. (2009). Fractional advection‐dispersion equations for modeling transport at the Earth surface. Journal of Geophysical Research: Earth Surface (2003–2012), 114(F4).
[23]Tsai, C. W., Hsu, Y., Lai, K. C., & Wu, N. K. (2014). Application of gambler’s ruin model to sediment transport problems. Journal of Hydrology, 510, 197-207.



QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top