Analysis of Questions B of American College Students Mathematical Contest in Modeling 2021

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2021 Beauty Contest title download: link: https://pan.baidu.com/s/1yFdg3vBMS4MY7CnQ3PMG9Q
extraction code: 6666

Original translation

2021 cubic meters
Question B: Fighting wildfires
Background
During the 2019-2020 Australian fire season, devastating wildfires occurred in every state, with New South Wales and eastern Victoria having the worst impact. Wildfires occur during severe droughts and persistent heat waves, and climate change has exacerbated this phenomenon. Figure 1 shows the wildfire hotspots in the area from October 1, 2019 to January 7, 2020. Yellow shows the fire from October 1st to January 6th and red shows fire on January 7, 2020 firefighters use none Human-machine surveillance and situational awareness (SSA) have been for several years; SSA drones carry high-definition and thermal imaging cameras and telemetry sensors to monitor and report data from front-line personnel wearable devices.
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  可穿戴设备可用作个人定位器信标或更复杂的环境监视器。SSA无人机帮助监测不断变化的情况,让应急行动中心(EOC)为最佳效果和最大安全提供最佳的指挥人员
  双向无线电通信允许“地面上的靴子”前进队向平机会提供状态报告,并允许平机会直

Then issue an order to the forward team. Deployers carry handheld two-way radios operating in the VHF/UHF bands.
The range of a handheld radio is limited by its low transmit power, usually a maximum of 5 watts, which mainly depends on
the distance of rural areas or "buildings" and the physical terrain of
urban areas"; weather has no effect on VHF/UHF signals Large. A 5-watt radio
has a nominal range of 5 kilometers on a flat, unobstructed ground, but it drops to 2 kilometers in urban areas.
Repeaters, transceivers, and automatic replay signals can be expanded at higher power Radio range. The repeater located between the front line and the EOC can relay radio signals from the front line to the EOC, and from the EOC to the front line. The range of the repeater also depends on the distance and terrain, but is significantly larger than the low-power handheld radio .
recently, hovering UAV mounted repeater is used to significantly increase the front low power radio range of a repeater 10 W, weight of 1.3 kg, hovering above the ground by the drone, can reach 20 km The range. Acme’s prototype Wile E-15.2X hybrid drone is expected to cost about $10,000 (AUD) when equipped with radio repeaters or video and telemetry capabilities. Tests have shown that this drone has a meter 1 The abilities listed.
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Requirements: Your consultant team has been retained to:

  1. Create a model to determine the optimal number and combination of SSA drones and radio repeater drones to purchase for a proposed new department of the Victorian National Fire Service (CFA), "Rapid Bush Fire Response"). Your model should balance capabilities and safety with economy, and consider the needs and terrain for observation and communication tasks. Your model should also take the size and frequency of fire events as parameters.
  2. Explain how your model adapts to the changing possibilities of extreme fire events in the next ten years. Assuming that the cost of the UAV system remains the same, predict what equipment cost will increase.
  3. Determine a model to optimize the position of hovering VHF/UHF radio repeater drones for fires of different sizes on different terrains, as shown in Figure 2: Topographic Map of Eastern Victoria. Please note that the elevation ranges from sea level on the coast to 1,986 meters of mountains. Bogon, Victoria.
  4. Prepare a two-page annotated budget request supported by your model for submission to the Victorian government.
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    Your PDF solution does not exceed 25 pages and should include:
  • One page summary table.
  • table of Contents.
  • Your solution.
  • Two-page annotated budget request.
  • List of references.
    Note: MCM competitions now have a 25 page limit. All aspects of your submission are calculated to a limit of 25 pages (summary form, table of contents, reference list and any appendices).
    The term
    "boots on the ground" advancing team: "boots on the ground" is an idiom that refers to the personnel at the place of action. In terms of fire protection, these are the lines of effort by the leading teams to control fire incidents; they have immediate and critical knowledge of the rapidly changing situation.
    Budget request: A budget request is a business letter
    seeking funding for the costs, expenses, and/or business overhead of a project or department within the organization . The annotated budget request provides a rationale or justification for each requested item.
    National Fire Services Agency (CFA):
    Volunteer Fire Services
    Emergency Operations Center (EOC) responsible for fire fighting, rescue and response to other accidents and hazards in most parts of Victoria, Australia : emergency-related actions and activities, and requests for activation and deployment of resources (personnel Or equipment)
    of the central command and control point). The mobile fair can be deployed near the emergency scene.
    Repeater: an unattended radio transceiver that
    automatically rebroadcasts the received signal at nearby frequencies (VHF ± 600k Hz (0.6 MHz) and UHF 5 MHz) or adjacent channels with high power.
    Situational awareness: the perception of the current elements of events, understanding their meaning, and inferring their status into the near
    future; in other words, knowledge and understanding of what is happening around you.
    Monitoring: Collect and analyze data systematically and share it with others
    who can take action on the information .
    Transceiver: A radio that can both send and receive.
    UHF: UHF, the radio frequency ranges from 300 MHz to 3000 MHz.
    VHF: VHF, the radio frequency ranges from 30 MHz to 300 MHz.

Thinking analysis

Question B Understanding
Question Center: Fighting Wildfires
Question Requirements:
(1) UAV purchase model.
A typical optimization problem, considering the economic and performance indicators of the UAV, to optimize the use of the current task. The focus is also on the innovation point: considering the relative position between the EOC observation point and the front line, how to optimize the distribution in space is also a key optimization goal.
(2) UAV working model The
second question is relatively simple, and simple questions can be done beautifully. Consider the extreme situation, and analyze the effect of the current (Q1) purchase plan, and in which aspect of the equipment cost needs to be increased, such as the battery cost caused by the flying distance? Signal transmission cost?
(3) UAV scheduling model
The terrain needs to be simplified when modeling the problem, but when drawing the map, you can consider using tools such as ArcGIS to produce the map, which is beautiful and novel. The problem center is to solve the UAV flight route or mission destination under different terrains and different fire levels. It is necessary to establish a scheduling model based on terrain and fire severity.
(4) According to the first three models, give the UAV purchase budget under different circumstances, and write a 2-page recommendation letter.
The highlight of this problem lies in the visual expression of the model, such as the drone dispatch process under different fire levels in Victoria.

Data download

Question B Australian Wildfire Dataset : Link: https://pan.baidu.com/s/1Kye3n683Bo7n6jPmKC0fkw
Extraction code: bshu

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