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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蔡宛珊 | |
| dc.contributor.author | Kung-Chung Lai | en |
| dc.contributor.author | 賴冠中 | zh_TW |
| dc.date.accessioned | 2021-06-16T23:04:48Z | - |
| dc.date.available | 2013-08-10 | |
| dc.date.copyright | 2012-08-10 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-08-06 | |
| dc.identifier.citation | References
[1]Ancey, C., Bohm, T., Jodeau, M., and Frey, P. (2006).“Statistical description of sediment transport experiments.” Phys Rev., E 74, 011302. [2]Ancey,C, A., Davison,C., Böhm, T.,Jodeau, M., and Frey, P.(2008).“Entrainment and motion of coarse particles in a shallow water stream down a steep slope.” J. Fluid Mech., 595, 83 – 114. [3]Bagnold, R.A., (1966).“An approach to the sediment transport problem for general physics.” Geological Survey Professional Paper 422-1, Washington, D.C. [4]Bradley, D.N., and Tucker, G.E. (2006).“Gambler's ruin and the residence time distribution in fluvial sediment dispersion.”Paper presented at American Geophysical Union fall meeting, San Francisco, December 2006. [5]C.W.Ahn and R.S.Ramakrishna.(2002).“A genetic algorithm for shortest path routing problem and the sizing of populations.”IEEE Trans. Evol.Comput., vol.6, pp. 566–579, Dec. [6]Cheng, N. S., and Chiew, Y. M. (1998). “Pick-up probability for sediment. entrainment.”J.Hydraul. Eng., 124(2), 232-235. [7]Einstein, H. A. (1937). “The bedload transport as probability problem.”Mitteilung der Versuchsanstalt fuer Wasserbau an der Eidgenössischen Technischen Hochschule.Zürich.110. [8]Einstein, H. A. (1950). “The bed load function for sediment transportation in open channel flow.” Technical bulletin no.1026, U.S. Dep.Of Agriculture, Washington,D.C. [9]Engelund, F. (1965).“A criterion for the occurrence of suspended load.” LaHouille Blanche, 8, 802. [10]Franceschini, S., Tsai, C., and Marani, M., (2012).“Point estimate methods based onTaylor Series Expansion – The perturbance moment method – A more coherentderivation of the second order statistical moment.” Appl. Math. Modell.,doi:10.1016/j.apm.2011.11.079. [11]Franceschini, S., and Tsai, C. (2010).“Assessment of uncertainty sources in water quality modeling in the Niagara River.”Adv. Water Resour. 33 (4) 493–503. [12]Hancock, G.S. and Anderson, R.S.(2002).“Numerical modeling of fluvial strath-terrace formation in response to oscillating climate.”GSA Bulletin, 114(9): 1131-1142. [13]G.Harik, E. Cant˘u-Paz, D.E.Goldberg, and B. L. Miller., (1999).“The Gambler’s ruin problem, genetic algorithms, and the sizing of populations.”Evol.Comput., vol. 7, pp. 231–253. [14]Kuai, K. Z., Tsai, C. “Stochastic modeling of nonuniform sediment transport under unsteady flow condition.” submitted to Water Resource. [15]Nin˜o, Y., Lopez, F., Garcia, M., (2003). “Threshold for particle entrainment into suspension.”Sedimentology 50, 247– 264. [16]Ross, S.M. (2000). “Introduction to probability models.”Academic Press, San Deigo, CA. [17]Samaga, B. R., Ranga Raju, K. G., and Garde, R. J., (1986a). “Bed load transport of sediment mixtures.”J. Hydraul. Eng., 112(11), 1003– 1018. [18]Samaga, B. R., Ranga Raju, K. G., and Garde, R.J., (1986b). “Suspended load transport of sediment mixtures.” J. Hydraul. Eng., 112(11), 1019– 1035. [19]Sun Z., (1989).“A stochastic model of sediment interchanges.”Journal of Sediment Research, (03), 1-9. [20]Sun, Z., and Donahue, J. (2000). “Statistically derived bedload formula for any fraction of nonuniform sediment.”J.Hydraul. Eng., 126(2), 105-111. [21]Yang, F. N. (2011) “Stochastic modeling of bedload transport by the continuous-time Markov Chain process.” M. S. thesis, Grad. Inst. of Civ. Eng., Natl. Taiwan Univ., Taipei. [22]Tung Y-K, Yen B.C.(2005). “Hydrosystems engineering uncertainty analysis.”New York: McGraw-Hill. [23]Wu, F.-C., and Chou, Y.-J.(2003a).“Rolling and lifting probabilities for sediment entrainment.” J. Hydraul. Eng., 129, 110– 119. [24]Wu, F.-C., and Yang, K.-H.(2004). “A stochastic partial transport model for mixed-size sediment: Application to assessment of fractional mobility.” Water Resour. Res., 40(4), w04501. [25]Van Rijn, L.C.(1984). “Sediment transport, Part II: Suspended load transport.”J. Hydraul. Eng.,110(11), 1613-1641. [26] 許盈松、蔡俊鋒、魏綺瑪、黃宏莆 (2007)，“水庫泥沙濁度與濃度率定關係研究－以石門水庫為例”，農業工程學報，第53卷，第1期，62-71. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/64871 | - |
| dc.description.abstract | 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。 | zh_TW |
| dc.description.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. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T23:04:48Z (GMT). No. of bitstreams: 1 ntu-101-R99521317-1.pdf: 2406030 bytes, checksum: 9f81737f0b81a5f1d44684199ce3964c (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | Contents
謝誌 | 摘要 Ⅱ Abstract Ⅲ Contents Ⅳ Figure list Ⅶ Table list Ⅷ Chapter1 Introduction 1 1.1 Problem Statement 1 1.2 Objective of Study 3 Chapter2 Literature Review 6 Chapter3 Three-state Continuous-time Markov Chain Model of Sediment Transport 12 3.1 Model Development 12 3.1.1 Introduction of Continuous-time Markov Chain 12 3.1.2 Three-state Continuous-time Markov Chain 14 3.1.3 Transition Probability Function 15 3.1.4 The Long-run Limiting Probability 17 3.1.5 Sediment Transport Rate 18 3.2 Determination of Parameters 19 3.2.1 Quantify the Sediment Particles 19 3.2.2 Mean Particle Velocity 20 3.2.3 Dimensionless Effective Shear Stress 21 3.2.4 Transition Probability Matrix 22 3.2.5 The Mean Transient Rate 24 3.3 Model Results and Data Validation 25 3.3.1 Flume Experiment of Samaga et al. (1986) 25 3.3.2 Model Calibration 26 3.3.3 Model Validation 30 3.3.4 Model Discussion 32 3.4 Summary 34 Chapter4 Gambler’s ruin Problem 35 4.1 Introduction of Gambler’s ruin Problem 35 4.1.1 The Gambler’s ruin Problem 35 4.1.2 Mean Time Spent in Transient States 36 4.2 First Case: Model Parameter Discussion 38 4.2.1 Application of Gambler’s ruin Problem to Sediment Transport Modeling 38 4.2.2 Number of Sediment Motion Particle 39 4.2.3 Determination of Parameters 41 4.2.4 Model Results and Discussion 43 4.3 Second Case: The Shihmen Reservoir Basin 48 4.3.1 Problem Statement 48 4.3.2 Model Development 49 4.3.3 Determination of Parameters 52 4.3.4 Uncertainty Analysis 54 4.3.5 Model Results and Discussion 57 4.4 Recommendation 62 4.5 Summary 62 Chapter5 Summary and Conclusion 64 References 69 Appendix 72 Figure List Figure 1.1 The schematic of sediment particle movement 3 Figure 3.1 Diagram of the mean transient rate versus dimensionless effective shear stress in M3 run 27 Figure 3.2 Diagram of the mean transient rate versus dimensionless effective shear stress in M3 run 28 Figure 3.3 Diagram of the mean transient rate versus dimensionless effective shear stress in M3 run 29 Figure 3.4 Comparison of calculated and measured bedload transport rate 31 Figure 3.5 Comparison of calculated and measured suspended load transport rate 31 Figure 3.6 Relation of bedload transport rate to time 33 Figure 3.7 Relation of suspended load transport rate to time 33 Figure 4.1 The schematic of the mean time spent in each transient state in Gambler’s ruin problem 38 Figure 4.2 The schematic of the application of sediment transport in Gambler’s ruin problem 39 Figure 4.3 The relation between the probability and the particle diameter 45 Figure 4.4 The probability to different maximum number of particles with different flow condition but same composition of sediment 46 Figure 4.5 Relation of mean time spent to number of particles 47 Figure 4.6 The Shihmen reservoir Basin 51 Figure 4.7 Effective risk of number of sediment particles in the water column in the time period of 2008 59 Figure 4.8 Effective risk of the mean value of the deterministic and the expected value computed for uncertainty variable 61 Figure 4.9 Results of one standard deviation interval about the expected value 61 Table List Table 1.1Previous study about particle interaction using Markov Chain method 11 Table 4.1 List of data used in this study 51 Table 4.2 Sediment concentration empirical formula 54 Table 4.3 Typhoon event occurred and the date of the storm warning in 2008 61 | |
| dc.language.iso | en | |
| dc.title | 以序率模式探討泥砂運動機制 | zh_TW |
| dc.title | Application of Continuous-time Markov Chain and
Gambler’s ruin Problem to Sediment Transport Modeling | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 卡艾瑋,吳富春 | |
| dc.subject.keyword | 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, | zh_TW |
| dc.subject.keyword | sediment particle interaction,stochastic model,uncertainty analysis,continuous-time Markov process,Gambler’s ruin problem, | en |
| dc.relation.page | 77 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-08-07 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
| 顯示於系所單位： | 土木工程學系 | |
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