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Problem B：Fighting Wildfires…
During the 2019-2020 fire season, wildfires have had a devastating impact on every state in Australia, especially New South Wales and the eastern part of Victoria. Wildfires usually occur during periods of severe drought and heat waves. Figure 1 shows the heat map of the mountain fires in this area from October 1, 2019 to January 7, 2020. The yellow color indicates that the mountain fires continued from October 1 to January 6, and the red color only indicates 2020. Wildfires were active on January 7.
Firefighters have used drones for surveillance and situational awareness (SSA) for many years. The high-definition, thermal imager and telemetry sensors carried by the SSA drone can monitor and report data from the wearable devices of frontline personnel. Among them, wearable devices can be used for personnel positioning and environmental monitoring. SSA drones are used to monitor the constantly changing situation on the spot, so that the Emergency Operations Center (EOC) can better, more efficiently and safely guide staff.
The two-way radio communicator allows forward troops on the ground to send status data reports to the EOC, while allowing the EOC to directly issue commands to forward troops. The deployed personnel carry handheld two-way radios operating in the VHF/UHF bands. The working range of hand-held radio equipment is limited by its low transmit power (usually 5 watts maximum), and is mainly determined by "distance and physical terrain in rural areas" or "building terrain in urban areas", where the weather affects VHF/ The impact of UHF is small. The nominal range of 5-watt radio equipment on flat areas and unobstructed ground is 5 kilometers, but only 2 kilometers in urban areas.
A repeater is a transceiver that automatically rebroadcasts signals with higher power, which can extend the working range of the radio. 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. Similarly, the working range of the repeater depends on the distance and terrain, but it is much larger than a low-power handheld radio.
Recently, hoverable drones with repeaters have been used to greatly expand the working range of frontline low-power radios. A UAV carrying a "10-watt, 1.3-kg repeater" can reach a working range of 20 kilometers at an altitude far above the ground. When the WileE-15.2X prototype drone is equipped with radio repeaters or video and telemetry capabilities, the estimated cost can reach 10,000 Australian dollars. Through testing, it is known that the UAV has the functions shown in Table 1.
Flight distance: 30 kilometers
Maximum speed: 20m/s
Maximum flight time: 2.5 hours
Charging time of the drone's built-in battery: 1.75 hours
Note: When the drone's built-in battery is charged, auxiliary batteries such as radio, video/telemetry, etc. can be used Replacement
(The implication is that the built-in battery of the drone is not allowed to be removed, so there is a "cooling" time, and it needs to be recycled and recharged. The batteries such as cameras, radios and other instruments can be removed to ensure that there is electricity at any time. Moreover, the question does not say The battery life of cameras and other instruments should be greater than 2.5 hours)
The requirements of this article are as follows:
- Establish a model for "CFA's new department-Wildfire Emergency Response Department" to purchase the optimal proportion of SSA drones and radio repeater drones. The model should balance its capabilities and safety while considering economy, as well as "reconnaissance communication mission requirements" and "terrain." The model should also take the size and frequency of fire events as parameters.
- Explain how your model adapts to possible changes in the "extreme wildfire events in the next ten years"? Assuming that the cost of drone equipment remains the same, which equipment costs are expected to increase?
- Design a model to optimize the location of VHF/UHF radio repeater drones with different fire sizes on different terrains, as shown in Figure 2: Topographic Map of East Victoria. Note that the altitude range refers to 1986 meters from the coast to sea level to the Bogong Mountains.
- Prepare an annotated budget form based on the model in this article to CFA.
Overview
There are two types of auxiliary equipment mentioned in the title, one is the SSA detector, which is used to monitor the two functions of "positioning", "communication" and "personal safety" of the ground forces; The communication range of the army's handheld radio. The functions of these two types of instruments cannot replace each other.
On the other hand, it can be seen from the question that the UAV can only carry one of the above two types of instruments, either with SSA or with repeater. (Original: Akme Corporation's prototype WileE–15.2X hybrid drone is projected to cost approximately $10,000 (AUD) when equipped with either a radio repeater or video & telemetry capability . Ten thousand Australian dollars can only carry SSA or can only carry repeaters, otherwise , I don’t know what the unit price of SSA or repeater is.)
Therefore, several key elements of this article:
UAV, repeater, SSA, fire size and frequency, cost, and terrain.
(The title does not limit the number of ground troops)
Question 1: Establish a model for "CFA's new department-Wildfire Emergency Response Department" to purchase the optimal proportion of SSA drones and radio repeater drones. The model should balance its capabilities and safety while considering economy, as well as "reconnaissance communication mission requirements" and "terrain." The model should also take the size and frequency of fire events as parameters.
Question 1 mainly needs to consider "how many drones and instruments should be bought under what circumstances". Therefore, the dependent variable can be set to "SSA and repeater", the drone does not need to be listed in the formula, because there is "SSA and repeater" must be equipped with a drone; and the independent variable can be set to "fire Situation scale and frequency" and "topography"; constraints can be set to "cost", "communication requirements", "location and monitoring and other capabilities". In this case, we can get a planning problem with constraints. (The cost of SSA and repeater can also be regarded as an objective function)
- The larger the scale of the fire, the greater the threat to personnel, so it is necessary to ensure that SSA can detect every member of the army; and the higher the frequency of the fire, the larger the communication range may be required to coordinate the location of personnel at any time and cooperate with each other;
- The more complex the terrain, the stronger the signal interference, so more repeaters are needed (here, an additional "signal interference model" should be established to simulate the impact of different terrain environments on the signal. Such problems should It has been explained in a paper);
- Also consider how many square kilometers the largest fire area is in the area, and the total number of drones purchased should cover all areas where fires may occur, that is, "saturation type";
In this way, a model can be established based on the relationship between the independent variable and the dependent variable, and the optimal solution can be found with reference to the constraint conditions. Similar to the "graphic method to calculate linear programming problem", there may be multiple solutions at the edge.
Question 2: Explain how your model adapts to possible changes in the "extreme wildfire event in the next ten years"? Assuming that the cost of the UAV system remains the same, which equipment costs are expected to increase?
"How your model adapts to the changing likelihood of extreme fire events over the next decade" can be understood as a change in the "scale and frequency" of wildfires.
Because the demand for SSA and repeaters will change after the scale and frequency change, it may be necessary to buy more SSAs and repeaters. (The topic is only to control costs, not necessarily a limit on the amount, but the less money the better)
Therefore, in this question, you can try to analyze the climate change in this area of Australia, see what the relationship between climate and fire conditions is in recent decades, and then predict what kind of situation the wild fires might take in the next ten years. After getting the scale and frequency of wildfires in the next ten years, it can be solved by substituting the formula of the first question.
So the main thing is to predict the climate.
Question 3: Design a model to optimize the location of VHF/UHF radio repeater drones with different fire sizes on different terrains, as shown in Figure 2: Topographic Map of East Victoria. Note that the altitude range refers to 1986 meters from the coast to sea level to the Bogong Mountains.
"Optimizing the position of the drone" means that the position of the drone can be adjusted as the terrain and fire conditions change.
The stronger the terrain interferes with the signal, the denser the repeater drones should be, and the fire has the same effect on the drones.
Among them, the working range of the repeater is based on half price, and the complexity of the terrain will reduce the half price unit, so the "UAV position-terrain" model can be established based on this; and the large scale of the fire requires SSA guarantee troops The safety of personnel must at least ensure that personnel within the fire range can be covered by the SSA, and the "UAV position-fire" model can be established accordingly.
Question 4: Prepare an annotated budget form based on the model in this article to CFA.
There is no special format specification for the annotated budget form, as long as the content required by the title is available. (Original: Budget Request: A budget request is a business letter seeking funds for costs, expenses, and/or operating overhead for a project or department within an organization. An annotated budget request provides a justification or rationale for each requested item.)