数学建模美赛o奖论文_精品文档.pdf

1、 For office use only T1 _ T2 _ T3 _ T4 _ Team Control Number 55069 Problem Chosen A For office use only F1 _ F2 _ F3 _ F4 _ 2017 MCM/ICM Summary Sheet The Rehabilitation of the Kariba Dam Recently,the Institute of Risk Management of South Africa has just warned that the Kariba dam is in desperate ne

2、ed of rehabilitation,otherwise the whole dam would collapse,putting 3.5 million people at risk.Aimed to look for the best strategy with the three options listed to maintain the dam,we employ AHP model to filter factors and determine two most influential criteria,including potential costs and benefit

3、s.With the weight of each criterion worked out,our model demonstrates that option 3 is the optimal choice.According to our choice,we are required to offer the recommendation as to the number and placement of the new dams.Regarding it as a set covering problem,we develop a multi-objective optimizatio

4、n model to minimize the number of smaller dams while improving the water resources management capacity.Applying TOPSIS evaluation method to get the demand of the electricity and water,we solve this problem with genetic algorithm and get an approximate optimal solution with 12 smaller dams and determ

5、ine the location of them.Taking the strategy for modulating the water flow into account,we construct a joint operation of dam system to simulate the relationship among the smaller dams with genetic algorithm approach.We define four kinds of year based on the Karibas climate data of climate,namely,no

6、rmal flow year,low flow year,high flow year and differential year.Finally,these statistics could help us simulate the water flow of each month in one year,then we obtain the water resources planning and modulating strategy.The sensitivity analysis of our model has pointed out that small alteration i

7、n our constraints(including removing an important city of the countries and changing the measurement of the economic development index etc.)affects the location of some of our dams slightly while the number of dams remains the same.Also we find that the output coefficient is not an important factor

8、for joint operation of the dam system,for the reason that the discharge index and the capacity index would not change a lot with the output coefficient changing.Team#55069 Page 2 of 2 Contents 1 Overview.1 1.1 Background.1 1.2 Restatement of the Problem.1 1.3 Literature Review.2 2 Assumptions and Ju

9、stifications.2 3 Notation.3 4 Model Overview.4 5 Model Theory.5 5.1 Determination of the Number and Location of the Dams.5 5.2 Joint operation of dam system model.9 6 Model Implementation and Results.11 6.1 The Number and Location.11 6.2 The Strategy of Modulating Water Flow.14 7 Sensitivity Analysi

10、s.15 7.1 The Model of Determination of the Number and Location.15 7.2 The Model of Modulating Water Flow.17 8 Further discussion.17 9 Strengths and Weaknesses.18 9.1 Strengths.18 9.2 Weaknesses.19 10 Conclusion.19 11 The Evaluation of Three Options.20 11.1 Establish a Hierarchical Model.20 11.2 Anal

11、ysis and Results.21 Team#55069 Page 1 of 28 1 Overview 1.1 Background A Zambezi River Authority conference was held in March 2014,engineers warned that the foundations of the dam had weakened and there was a possibility of dam failure unless repairs were made.On 3 October 2014 the BBC reported that“

12、The Kariba Dam is in a dangerous state.Opened in 1959,it was built on a seemingly solid bed of basalt.However,in the past 50 years,the torrents from the spillway have eroded that bedrock,carving a vast crater that has undercut the dams foundations,engineers are now warning that without urgent repair

13、s,the whole dam will collapse.If that happened,a tsunami-like wall of water would rip through the Zambezi valley,reaching the Mozambique border within eight hours.The torrent would overwhelm Mozambiques Cahora Bassa Dam and knock out 40%of southern Africas hydroelectric capacity.Along with the devas

14、tation of wildlife in the valley,the Zambezi River Authority estimates that the live of 3.5 million people are at risk.”On February 2015,Engineers have started on a R3.3bn rescue marathon to prevent the“catastrophic failure”of the Kariba Dam.According to a World Bank special report on the beleaguere

15、d structure-one of the biggest man-made dams in the world-a potential wall collapse threatens the lives of about 3-million people living on the Zambezi River floodplain between the hydro scheme on the Zambia-Zimbabwe border and the Mozambique coast.1 1.2 Restatement of the Problem We are required to

16、 provide an overview of potential costs and benefits with the three options already listed.Then we need to establish a model to determine the number and placement of the new dams when removing the Kariba dam along the Zambezi River.The same overall water management capabilities are also needed.In addition,we should consider emergency water flow situations and restrictions regarding the locations and time,so that we could give out the strategy for modulating the water flow through our new multipl