2021 MCM Problem B: Wisdom Fights Wildfire
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background:
During the 2019-2020 fire prevention period, all Australian states were ravaged by wildfires, which had a devastating impact on New South Wales and East Victoria. Forest fires occur when the seasons alternate between severely dry and persistently high temperatures.
Figure 1 shows the hot spots where forest fires occurred from October 1, 2019 to January 7, 2020. Yellow indicates the fire from October 1 to January 6, and red indicates the fire on January 7, 2020. Active fire.
Firefighters have used remote-controlled aircraft to monitor and sense fire (SSA) for several years. SSA carries high-definition cameras with red heat detection functions and remote sensing sensors to monitor and obtain data from wearable devices on frontline workers.
Wearable devices can be used in personnel positioning and more complex environmental monitoring.
SSA UAV can help monitor the development situation, so that EOC can command all staff and have the best effect and maximum safety.
The communication of two-way wireless walkie-talkies allows the "ground operations" frontline team to provide status reports for EOC and enables EOC (Emergency Operations Center) to guide the work of the frontline team. Deployment personnel carry handheld two-way wireless walkie-talkies to operate in UHF/VHF bands , The communication range of the handheld walkie-talkie is limited by its low transmit power, nominally 5W. Its communication range mainly depends on the distance and terrain in rural areas, and mainly depends on the shelter of buildings in urban areas. The weather has a weak influence on UHF/VHF. A walkie-talkie with a power of 5W can nominally spread 5KM on flat ground, but can only spread 2KM in cities. Repeater is a radio that can automatically broadcast at higher power. Signal transceiver, used to extend the radio communication range. The repeater located between the front line and the EOC can transmit radio signals from the front line to the EOC and from the EOC to the front line at the same time . The range of the repeater also depends on the distance and terrain, but it is significantly stronger than the lower power handheld walkie-talkies.
Not long ago, drones carrying repeaters have been used to automatically extend the communication range of low-power walkie-talkies. The 10W repeater carried by drones weighs 1.3 kilograms, hovering much higher than the ground, and can be extended to 20 The communication range of kilometers . Akme’s prototype WileE – 15.2 times the hybrid drone is expected to cost about US$10,000 (AUD)
With radio repeater or video and telemetry functions.
Tests have shown that this drone has the functions listed in Table 1.
Requirements: Your consultant team should complete the following tasks:
1 Create a model to determine the optimal number and combination of SSA drones and radio repeater drones to purchase drones for a new department in Victoria's "Rapid Bushfire Response" program. Your model should balance capabilities 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.
Considering that the optimal number and combination are required in the title , the focus is on the best two words, so the linear/non-linear programming method is mainly considered. Here, LINGO is recommended. The dependent variable is the number and combination of various types of drones. , The independent variables are about the size of the fire (scale, you can roughly classify the fire level based on the information available on the Internet), the frequency of occurrence, and the topography (which can be viewed by region (urban/rural ratio), and the topographic features are compared with the radio walkie-talkie The communication range is linked into a formula). Constraints can include costs, the scope of communication required, and the proportion of staff that can be covered to all staff
The higher the coverage factor, the wider the coverage, the better, and the lower the cost, the better. A formula can be constructed,
MAX{ coverage factor * coverage cost }
Claim:
- Coverage ≥ Fire Range
- The entire UAV system can be used reasonably under different terrain conditions
- UAVs must have a certain amount of redundancy, because when UAVs are out of power, they need to be replaced. At the same time, UAVs need to take on the replacement task. The fastest full update time of UAVs ≥ the next fire Minimum interval
Establishing such a formula first needs to quantify all the changes. In addition, factor analysis can be used to weight different constraints to analyze the optimal choice under different weighting methods.
The idea of solving the problem of the following three questions will be updated in the WeChat public account (Technical House Xiaobei)
3 Determine a model for optimizing the location of UHF radio relay drones to respond to fires of different scales on different terrain (Figure 2: Topographic Map of Eastern Victoria). Please note that the elevation ranges from sea level on the coast to 1986 meters at Mount Bogon in Victoria.
4 Based on your model, write a one to two page annotated budget request for CFA to submit to the Victorian government