Question B: The
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Background
Australia's 2019-2020 fire season has caused devastating wildfires in every state, with the greatest impact on New South Wales and eastern Victoria. Wildfires occur during severe droughts and persistent heat waves, which are exacerbated by climate change. Figure 1 shows the wildfire hotspots in the area from October 1, 2019 to January 7, 2020. Yellow indicates the fire from October 1 to January 6, and red indicates the active fire on January 7, 2020. .
Firefighters have used drones for surveillance and situational awareness (SSA) for several years; SSA drones carry high-definition and thermal imaging cameras and telemetry sensors to monitor and report data from wearable devices of frontline personnel.
Wearable devices can be used as personal location beacons or more complex environmental monitors. SSA drones can help monitor changing conditions, enabling the Emergency Operations Center (EOC) to best guide active crews for best results and maximum safety.
Figure 1. Wildfire hotspots in southeastern Australia, October 1, 2019 to January 7, 2020. Source: Australian Government Meteorological Service, National Aeronautics and Space Administration Resource Management System fire information.
Two-way radio communication allows the "ground start" forward team to provide status reports to the EOC, and allows the EOC to directly issue commands to the forward team. The deployed personnel carry a handheld two-way radio operating in the VHF/UHF band. The range of a handheld radio is limited by its low transmit power (usually a maximum of 5 watts), and mainly depends on the distance of rural areas or "buildings" and the physical terrain of
urban areas; the weather has a great influence on VHF/UHF signals. small. The nominal range of a 5-watt radio on a flat, unobstructed ground is 5 kilometers, but it drops to 2 kilometers in urban areas.
A repeater is a transceiver that automatically rebroadcasts signals with higher power, which can extend the radio range. The repeater located between the front line and the EOC can relay radio signals from the front line to the EOC, or from the EOC to the front line. The range of the repeater is also determined by distance and terrain, but it is much larger than a low-power handheld radio.
Recently, hovering drones with repeaters have been used to greatly extend the range of frontline low-power radios. A 10-watt heavy transmitter, weighing 1.3 kilograms, is suspended from a drone far above the ground and can reach a range of 20 kilometers. When Akme Corporation’s prototype WileE-15.2X hybrid drone is equipped with radio repeaters or video and telemetry capabilities, it is expected to cost approximately US$10,000. Tests show that the drone has the functions listed in Table 1.
Table 1. WileE-15.2X Hybrid UAV features
Flying range: 30 kilometers Maximum speed: 20 m/s Maximum flight time: 2.50 hours The
built-in battery charging time is 1.75 hours.
Note: When the built-in battery is charging, the radio or video/telemetry auxiliary battery can be exchanged.
Requirements: Your consultant team has been reserved to:
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Create a model to determine the optimal number and mix of SSA drones and Radio Repeater drones to be purchased for the new department "Rapid Bushfire Response" proposed by the Victorian National Fire Service (CFA). Your model should strike a balance between capability and safety and 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.
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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 unchanged, what equipment cost increase is expected to occur.
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Determine a model to optimize the location of VHF/UHF radio relay drones for fires of different sizes on different terrains, as shown in Figure 2: Topographic Map of Eastern Victoria. Please note that the altitude ranges from sea level on the coast to 1,986 meters at Mt. Victoria Bogong.
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Prepare a one to two page annotated budget request supported by your model for CFA submission to the Victorian government.
Figure 2: Topographic map of East Victoria WWW.FREEWORLDMAPS.NET
Your PDF solution (with no more than 25 pages in total) should include:
• A one-page summary table.
• table of Contents.
• Your complete solution.
• One to two pages of annotated budget request.
• List of references.
Note: MCM contests are now limited to 25 pages. All your submissions count towards the 25 page limit (summary form, table of contents, reference list and any appendices).
Glossary
"Boots on the ground" forward team: The idiom "boots on the ground" means the actual personnel at the place of action. In terms of fire protection, these teams are at the forefront of
fire control efforts; they have a direct and critical understanding of rapidly changing conditions.
Budget request: A budget request is a business letter designed to seek funding for the costs, expenses, and/or operating expenses of a project or department in the organization. Annotated budget requests provide a rationale or justification for each requested item.
National Fire Services Agency (CFA): Voluntary fire service, responsible for fire fighting, rescue and response to other accidents and hazards in most states of Victoria, Australia
Emergency Operations Center (EOC): The central command and control point, used for emergency-related operations and activities, and requests for activation and deployment of resources (personnel or equipment). Mobile EOC can be deployed near emergency situations.
Repeater: An unattended radio transceiver that can automatically rebroadcast the received signal with high power on nearby frequencies (VHF is ±600kHz (0.6 MHz), UHF is ±5MHz) or on adjacent channels.
Awareness of the situation: Perceive the current elements of the event, understand its importance, and infer its state into the near future; in other words, your knowledge and understanding of the surrounding situation.
Monitoring: Collect and analyze data systematically and share it with others who can take action based on the information.
Transceiver: A radio that can transmit and receive at the same time.
UHF: UHF, a radio frequency from 300 MHz to 3,000 MHz.
VHF: VHF, radio frequency from 30 MHz to 300 MHz.
Update ideas. Solve
The following is an excerpt from a book, you can find it, what is not clear.
Rescue costs can be divided into two parts: one part is the consumption of fire-fighting equipment and the salaries of firefighters, etc., which are related to the number of team members and the time spent fighting the fire; the other part is a one-time expenditure for transporting team members and equipment, which is only related to the number of team members
.Model assumptions . It is necessary to make assumptions in the form of the loss cost of burning the forest, the rescue cost and the degree of wildfire spread in dB/dt.
1. The loss fee is proportional to the forest burned area B(t), and the proportional coefficient is c. It is the cost of burning the unit area.
2. During the time from the fire to the start of fire fighting (0≤t≤t), the degree of fire spread is proportional to the time t, and the proportional coefficient β is the fire spread speed.
3. Send out x number of firefighters. After the firefighting starts (t> t), the spreading speed of the fire will be reduced to β-inx, where in-can can be regarded as the average fire-fighting speed of each team member. Obviously β<inx.
4. The cost per unit time of each firefighter is c, so the firefighting cost of each team member is e(tt); the one-time expenditure of each team member is c,
-the assumption of Article ⒉ can be explained as follows: the fire is centered on the fire point , It spreads roundly around at a uniform speed, so the radius r of the spread is proportional to the time t. And because the burned area B is proportional to Р, so B is proportional to t?, which is proportional to t. This assumption is based on wind It is generally reasonable under small conditions.
The reference model for question B has been updated in the group file.
