For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________
Team Control Number
For office use only F1 ________________ F2 ________________
66666
Problem Chosen
F3 ________________ F4 ________________
A
2017
Mathematical Contest in Modeling (MCM/ICM) Summary Sheet
The Kariba Dam on the Zambezi River is one of the larger dams in Africa. Its construction was controversial, and a 2015 report by the Institute of Risk Management of South Africa included a warning that the dam is in dire need of maintenance. A number of options are available to the Zambezi River Authority (ZRA) that might address the situation.
It is assumed that the design parameters, site selection and construction of the dam (dam group) after repair, reconstruction and reconstruction are in accordance with the requirements of water conservancy and hydropower projects. The number and location of the dam groups are in line with the requirements of water conservancy and hydropower projects. Therefore, the research problems are: a) Comparing the comprehensive benefits of the dams after restoration, reconstruction and reconstruction, establishing the mathematical model, and expounding the costs and benefits of each case; b) Reconstructing the dams (rebuilding the existing dams 10-20 A little dam), in the drought, heavy rain, moderate rain, light rain, when the water storage, flood discharge to ensure the probability of dam break the smallest, that is, dam group risk decision optimization.
For the first problem, this paper chooses the optimal cost and benefit plan for Kaliba Dam restoration work by establishing the economic benefit model, the economic loss model, the comprehensive benefit model, the absolute return model after restoration and the investment payback period model.
The cost-effectiveness of the three programs was evaluated in detail according to the results of the mathematical model. Option1, the restoration of the dam can extend the useful life of 11 years. While the one-time cost of access to the investment recovery period of 3.2 years. Option2, 100 years after the design of the reconstruction, the investment recovery period of 65.2 years. Option3, after rebuilding for the dam group, designed to use 100 years, the investment recovery period of 47.8 years. Three programs have better benefits, of which the best overall benefits of the three programs.
For the problem 1, this paper uses the R language software to draw the heatmap to validate the conclusion. Using the Matlab software to build the MSE model, the error analysis of the above results is further proved to be the best.
For the second problem, we use MATLAB and SPSS MODELER software to establish Author Topic Model, BP network and LS-SVM model to validate the LDA
model, and use MSE and ABS method to analyze the error of LDA model. The results show that the LDA model is accurate and reliable, and the error is small. It further shows that the mathematical model established in this paper has a certain generalization ability.
Key words: The zambezi river ；Kariba dam ; Water conservancy ; reconstruction
I. Introduction
In order to indicate managing the Zambezi river, the following background is worth mentioning.
1.1Zambezi River
The Zambezi (also spelled Zambeze and Zambesi) is the fourth-longest river in Africa, the longest east-flowing river in Africa and the largest flowing into the Indian Ocean from Africa. The area of its basin is 1,390,000 square kilometres (540,000 sq mi),[1][2] slightly less than half that of the Nile. The 2,574-kilometre-long river (1,599 mi) rises in Zambia and flows through eastern Angola, along the eastern border of Namibia and the northern border of Botswana, then along the border between Zambia and Zimbabwe to Mozambique, where it crosses the country to empty into the Indian Ocean.
From Victoria to the Falls for the upper reaches of Victoria Falls, 1287 km long; from Victoria Falls to the territory of Mozambique Kabula Bassa reservoir for the middle, 869 km long; Cabra Bassa is the following downstream, 579 km long.
Zambezi average slope of 0.4 ‰, runoff of 223.2 billion cubic meters, second only to the Congo River, ranked second in Africa.
1.2Kariba DamConstruction
The double curvature concrete arch dam was designed by Coyne et Bellier and constructed between 1955 and 1959 by Impresit of Italy[2] at a cost of $135,000,000 for the first stage with only the Kariba South power cavern. Final construction and the addition of the Kariba North Power cavern by Mitchell Construction[3] was not completed until 1977 due to largely political problems for a total cost of $480,000,000. During construction, 86 men lost their lives.[2][4]
The grassland in the floodplains around the Zambezi River relies on annual floods and seasonal rainfall, while rainfall in the region is richer than in the very dry west. Floods and vegetation expansion during the rainy season is limited in the north of the Zambezi River, indicating an increase in the northern margin of the floodplain. These vegetation provide food for numerous fish and animal species.
1.3 Kariba Dam
Kariba hydropower station is located in the African Zambia and Zimbabwe at the junction of the Zambezi (Zambezi) River Kariba Gorge, 290km away from Solihey, the project is mainly for power generation.
The dam site is composed of Precambrian rocks. The whole bed, the left bank and the right bank of the lower two-thirds of the height below are metamorphic biotite gneiss, gray and white surface with white stripes, foliation showing a bend. Rock outcrops in the river bed are hard, fine fractures, the depth of rock erosion between the two sides of 4.5 ~ 6m, susceptible to weathering. The upper part of the right bank is hard brown quartzite, with fractures developed, weathered biotite gneiss intrusions, and granitic granites appearing veins. Gneiss is almost entirely biotite lens body, due to the distribution is not wide, the underground project will not have a significant impact.
On November 11, 2013 It was announced by Zimbabwe's Finance Minister, Patrick Chinamasa that capacity at the Zimbabwean (South) Kariba hydropower station would be increased by 300 megawatts. The cost of upgrading the facility has been supported by a $319m loan from China. The deal is a clear example of Zimbabwe's \East\policy which was adopted after falling out with Western powers.[7] Construction on the Kariba South expansion began in mid-2014 and is expect to be complete in 2019.[8]
The north station belonging to Zambia has been in operation since 1976, and has four generators of 150 megawatts (200,000 hp) each for a total of 600 megawatts (800,000 hp); work to expand this capacity by an additional 360 megawatts (480,000 hp) to 960 megawatts (1,290,000 hp) was completed in December 2013. Two additional 180 MW generators were added.[9][10][11]
Figure 1.1 zambezi river kariba dam
1.4Kariba DamRecent activity
On the 6th of February 2008, the BBC reported that heavy rain might lead to a release of water from the dam, which would force 50,000 people downstream to evacuate. Rising levels led to the opening of the floodgates in March 2010, requiring the evacuation of 130,000 people who lived in the floodplain, and causing concerns that flooding may spread to nearby areas.
In January 2016 it was reported that water levels at the dam had dropped to 12% of capacity. Levels fell by 5.58 metres (18.3 ft), which is just 1.75 metres (5 ft 9 in) above the minimum operating level for hydropower. Low rainfalls and overuse of the water by the power plants have left the reservoir near empty, raising the prospect that both Zimbabwe and Zambia will face water shortages.
1.5The removal of the dam, restoration and reconstruction
The Kariba Dam on the Zambezi River is one of the larger dams in Africa. Its construction was controversial, and a 2015 report by the Institute of Risk Management of South Africa included a warning that the dam is in dire need of maintenance. A number of options are available to the Zambezi River Authority (ZRA) that might address the situation. Three options in particular are of interest to ZRA:(Option 1) Repairing the existing Kariba Dam, (Option 2) Rebuilding the
existing Kariba Dam, or (Option 3) Removing the Kariba Dam and replacing it with a series of ten to twenty smaller dams along the Zambezi River.
II. The Description of the Problem
2.1 Model Assumptions
1) Assuming that the design parameters, site selection and construction of the dam (dam group) after restoration, reconstruction and reconstruction are in accordance with the requirements of water conservancy and hydropower projects. The number and location of the dam groups are in line with the requirements of water conservancy and hydropower projects. Therefore, the research problems are: a) Comparing the comprehensive benefits of the dams after restoration, reconstruction and reconstruction, establishing the mathematical model, and expounding the costs and benefits of each case; b) Reconstructing the dams (rebuilding the existing dams 10-20 A little dam), in the case of drought, heavy rain, moderate rain and light rain, when the impoundment and flood discharge can ensure the probability of dam break, the risk decision of dam group is optimized.
2) The risk of flood discharge in emergencies is high, and this study does not consider the situation of emergency flood discharge.
3) Assuming the ecological restoration of the water-level drawdown area after the demolition of the dam, construction waste transportation and sediment deposition are ideal.
4) Assuming that the probability of dam break after rainfall to a certain water level is fixed.
5) Assume that the rainfall is a continuous variable, obeying the normal distribution.
6) Assuming that the dam group is a series model, do not consider the parallel and mixed
2.2 Equirement 1.
The annual economic benefits of the dam are made up of a number of benefits. These include power generation benefits, water supply benefits, irrigation benefits, shipping benefits, the value of flood storage, cultural tourism value, biological benefits, environmental benefits and so on. As a result of the various benefits, especially the power generation efficiency is changing year by year.
The annual economic losses caused by the dam include food production, fishery production, organic matter production, soil erosion control, ecological restoration, dam maintenance, reservoir dredging, water treatment, species loss, loss of cultural relics.
2.3 Equirement 2