没有合适的资源?快使用搜索试试~ 我知道了~
2024年美赛35篇特等奖O奖论文-D-2429211.pdf
1.该资源内容由用户上传,如若侵权请联系客服进行举报
2.虚拟产品一经售出概不退款(资源遇到问题,请及时私信上传者)
2.虚拟产品一经售出概不退款(资源遇到问题,请及时私信上传者)
版权申诉
0 下载量 89 浏览量
2024-05-06
11:41:32
上传
评论
收藏 2.96MB PDF 举报
温馨提示
![preview](https://dl-preview.csdnimg.cn/89271451/0001-4b33dd57b815a544697e84005acbdcc7_thumbnail.jpeg)
![preview-icon](https://csdnimg.cn/release/downloadcmsfe/public/img/scale.ab9e0183.png)
试读
25页
大学生,数学建模,美国大学生数学建模竞赛,MCM/ICM,2024年美赛特等奖O奖论文
资源推荐
资源详情
资源评论
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![](https://csdnimg.cn/release/download_crawler_static/89271451/bg1.jpg)
Problem Chosen
D
2024
MCM/ICM
Summary Sheet
Team Control Number
2429211
Dynamic Dams Model: A Multigranular, Human-Centered Approach For
Modeling Water In The Great Lakes
Summary
The Great Lakes serve as the heart of North America with their ebbs and flows providing the
lifeblood of both the surrounding environment and societies. Because of the lake’s incredible
importance, it is in the best interest of the world to protect them. Plan 2014, proposed by the
International Joint Committee (IJC), manages the water in the Great Lakes by building up water
behind both the Compensating Works dam at the Sault St. Marie River and Moses-Saunders dam
and taking action as needed. To better serve the Great Lakes region, we seek to expand Plan 2014
to regulate water levels optimizing for human needs and the preservation of ecosystems.
To determine optimal dam scheduling we modeled the Great Lakes as a dynamic flow network
and created two control algorithms that utilize linear programming to solve for optimal dam
schedules and water levels. The first control algorithm determines the optimal water level in each
lake that is achievable through use of the Compensating Works and Moses-Saunders dams over the
course of a multiple-month time horizon. After the optimal water levels have been determined, we
employ another control algorithm to plan how to schedule the dams over a daily time horizon to
achieve the water levels that equitably benefit stakeholders, but still adhere to the larger schedule. By
utilizing these two control algorithms, it is possible to generate dam schedules that meet stakeholder
needs while avoiding catastrophic events like flooding or dangerously low water levels.
An important aspect of our model is that it is mechanistic. Since we model real flows, it is
important to determine accurate parameters to encode natural and artificial processes. However,
the Great Lakes are a highly complex system, and they are influenced by several stochastic and
highly volatile processes. To account for this complexity, we utilized a data-based approach to best
coincide with the data that the IJC will have access to. By utilizing time lagged cross-correlation,
we were able to determine the relationship of flow rates between Great Lakes. We also utilized
linear regression to model the relationship between the height of each Great Lake and the rate
of flow in its distributaries. This allowed us to include necessary complexities while maintaining
accurate and faithful parameters.
Our model provides a number of key insights into effective management of the Great Lakes. We
observe that using adaptive control algorithms, it is possible to determine schedules that avoid
flooding in most cases and allow the IJC to be prepared when flooding is inevitable and to influence
the location and time of the flood. Moreover, we observe that despite the large amount of time it
takes for Lake Ontario to experience the effects of changes in Lake Superior, it is crucial to manage
Lake Superior with the downstream effects on Lake Ontario in mind. When Lake Ontario faces a
challenging climate event, effective scheduling at Lake Superior can mitigate the damage and allow
Lake Ontario to maintain optimal water levels.
Keywords: Linear Program; Dynamic Flow Network; Human-Centered; Multigranular Approach.
![](https://csdnimg.cn/release/download_crawler_static/89271451/bg2.jpg)
Team # 2429211 Page 2 of 24
Contents
1 Introduction 3
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Restatement Of The Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Overview of Linear Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Assumptions And Justifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Macroschedule Model 6
2.1 Dynamic Network Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Ideal Water Determination Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Linear Program Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Methods for Stakeholder Management . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Data-Based Model Of The Hydrosphere . . . . . . . . . . . . . . . . . . . . . . . 10
2.6 Additional Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Microschedule Model 12
4 Model Insights 13
4.1 Dynamic Control Of The System . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2 Robustness to Severe Climate Events . . . . . . . . . . . . . . . . . . . . . . . . . 15
5 Sensitivity Analysis 16
6 Conclusions 17
6.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7 Future Exploration 19
8 Memo To The IJC 20
A Notation 21
![](https://csdnimg.cn/release/download_crawler_static/89271451/bg3.jpg)
Team # 2429211 Page 3 of 24
1 Introduction
1.1 Background
Figure 1: A cloudless view of all of the Great
Lakes taken by a NASA satellite in August 2010
[13].
The Great Lakes are one of the most promi-
nent features of the North American continent;
they not only make up 20 percent of the world’s
freshwater, but they also have a tremendous im-
pact on the economy, climate, and ecosystems
of the United States and Canada. The Great
Lakes region is one of the largest economies
in the world, supporting 1.5 million people and
forming the backbone for other industries which
are valued at over 6 trillion dollars [8]. Addi-
tionally, they also are the source of life for over
3500 species of plants and animals across a
wide range of biomes making them indispens-
able to the North American ecosystems [18].
Due to the invaluable benefit that the Great
Lakes provide us, it is of the utmost importance
to society that they are flourishing in the best
way possible.
To ensure that the Great Lakes community is well-serviced, it is necessary to analyze the impacts
on the stakeholders dependent on the lakes. The stakeholders identified in the report by the Inter-
national Joint Committee (IJC) are: domestic water supply, commercial navigation, hydropower,
environment, recreational boaters, docking companies, and shoreline (riparian) property owners
[10].
The current methodology of managing the water flow in Lake Ontario is based on Plan 2014.
Plan 2014 prioritizes natural flow out of Lake Ontario into the St. Lawrence River while continually
checking if a number of critical points have been reached. When a critical point has been reached,
the IJC takes action to control the level of water in the dam [2]. After the initiation of Plan 2014
in 2017, record precipitation hit the area and Lake Ontario experienced severe flooding [7]. This
caused millions of dollars of damage and increased the risk for invasive species (like zebra mussels),
harmful algae bloom, and sewage blockage [15] [19] [10]. This event brought the effectiveness of
the plan under scrutiny. Flooding has proven to be a continual threat to the lives and livelihoods
of the stakeholders. Thus, ICM has set out to formulate water level control mechanisms that could
prevent such dire events.
1.2 Restatement Of The Question
To address the concerns of the IJC, we propose a number of human-centered algorithms that
control the water levels of the Great Lakes to best address the residents’ concerns around Lake
Ontario and the St. Lawrence River. Our models and algorithms are fit to address the needs of
various stakeholders, while ensuring that the water levels within the lakes remain safe. Motivated
by the flooding damage from 2017, our model focuses on achieving water levels and currents that
![](https://csdnimg.cn/release/download_crawler_static/89271451/bg4.jpg)
Team # 2429211 Page 4 of 24
benefit the stakeholders subject to hard constraints on the risk of flooding and low-water levels. Our
outlook differs significantly from that of Plan 2014 to be more resilient in a highly volatile climate.
We propose using a linear program to model the needs of the stakeholders with respect to the water
level and modulating it with dynamic control of dams that account for the transportation times of
the water. Inspired by the successes of Plan 2014 as a method to solve a complex constrained
scheduling problem and equipped with the knowledge of where Plan 2014 falls short, we propose
a model that utilizes the Compensating Works dam at the Sault. St. Marie River as well as the
Moses-Saunders dam to do the following:
1. Center the human impacts by modeling the needs of the stakeholders
2. Robustness to severe climate events
3. Dynamic control of the system
1.3 Overview of Linear Programs
Our control algorithms are implemented as linear programs. Linear programming is a widely-
used optimization technique in the field of operations research and network science. It has various
applications from policymaking to power plant deployment to production logistics to watershed
management [11, 20]. Linear programs rapidly found applications across the natural sciences,
industry, government, and many other fields, and are a natural way to model many scheduling
problems where it is important to understand how to plan a series of actions to maximize an
objective (typically profit or some other measure of overall utility) subject to some constraints (e.g.
there might only be so much time available to us) [21]. Within the realm of environmental decisions,
linear programming has been applied to solve complex questions like green-energy planning [5].
Inspired by the success of linear programs in related fields, our control algorithms employ linear
programming to determine how to utilize the dams within the Great Lakes. The advantages to be
expected from utilizing linear programming are as follows:
• Algorithms for solving linear programs are widely available and extremely fast. Due to the
effectiveness of the famous Simplex algorithm and its variants, linear programs can be solved
with incredible speed which is advantageous for testing out a variety of weather scenarios.
• Linear programs are interpretable. Practitioners need access to a white-box control algo-
rithm where it is possible to understand their decision.
• Linear programs are not defined with specific parameter values in mind. If practitioners need
to revise their predictions for environmental factors, they can easily rerun the model with the
adjusted parameters.
However, it’s also important to acknowledge the downsides that accompany linear programs:
• The objective and constraints must be linear. This limits the ways we can model our system
considerably and, as such, it is important to recognize parts of the model that are remnants
of the required linearity.
![](https://csdnimg.cn/release/download_crawler_static/89271451/bg5.jpg)
Team # 2429211 Page 5 of 24
• When a linear program is impossible to solve, it is difficult to visualize what is going wrong.
If our control algorithms determine that there is no valid schedule that meets all constraints,
it will be difficult for the practitioner to find a way to determine a valid schedule.
By keeping these disadvantages in mind, we designed our control algorithms to be effective even
with the drawbacks of linear programming.
1.4 Assumptions And Justifications
As mentioned in the problem statement, the dynamic network flow problem is wicked. As such,
we make use of several assumptions to manage the complexity of our models.
↓
i
W
Figure 2: Since water levels do not vary
much relative to total depth, we can approxi-
mate the lake surface area as being constant.
We can then convert flow to marginal height
by dividing by surface area.
Hydrology: The lake’s sizes remain con-
stant and our system can be simplified
to five nodes by not factoring in the
auxiliaries like lake St. Claire.
Justification: Keeping the lake sizes con-
stant provides us with a consistent con-
version metric, as seen in figure 2 be-
tween flow and height for each lake.
Based on the correlation data for the
flow rates, the other nodes are negligi-
ble as compared to the main outflows
between the Great Lakes.
Systemic: Dams can be fully opened or closed within an hour and they have zero downtime.
Additionally, the lag times calculated from correlation data are accurate (Figure 2).
Justification: We want to encapsulate granular dam schedules to minimize flooding and drought of
the Great Lakes community. Also, we need the lag times to be accurate to simulate the water
flowing between the lakes.
Scaling: The regressions we found for the flow rates from the lakes are linear (Figure 3) and the
time horizon of the data is on the order of a few months.
Justification: The regressions are done on the order of the change in height of the lakes, so the
flow rates for our purposes should be accurate. Since the time scale of our time lags is on the
order of a few months, our time horizon encapsulates the lag time and our model should be
used dynamically based on current data.
剩余24页未读,继续阅读
资源评论
![avatar-default](https://csdnimg.cn/release/downloadcmsfe/public/img/lazyLogo2.1882d7f4.png)
![avatar](https://profile-avatar.csdnimg.cn/fcd62adb0120465d9af280215b0ff722_snowtshan.jpg!1)
阿拉伯梳子
- 粉丝: 1665
- 资源: 5735
上传资源 快速赚钱
我的内容管理 展开
我的资源 快来上传第一个资源
我的收益
登录查看自己的收益我的积分 登录查看自己的积分
我的C币 登录后查看C币余额
我的收藏
我的下载
下载帮助
![voice](https://csdnimg.cn/release/downloadcmsfe/public/img/voice.245cc511.png)
![center-task](https://csdnimg.cn/release/downloadcmsfe/public/img/center-task.c2eda91a.png)
安全验证
文档复制为VIP权益,开通VIP直接复制
![dialog-icon](https://csdnimg.cn/release/downloadcmsfe/public/img/green-success.6a4acb44.png)