2024年MCM/ICM美國大學(xué)生數(shù)學(xué)建模競賽B題中英版發(fā)布

2024年美賽競賽時(shí)間為2024年2月2日早晨6點(diǎn)-2月6日早晨9點(diǎn)，2024年MCM/ICM美國大學(xué)生數(shù)學(xué)建模競賽B題中英版一起來看看。

中文賽題：搜尋潛水器

希臘的海上巡游迷你潛艇公司（MCMS）制造能夠?qū)⑷祟愡\(yùn)送到海洋最深處的潛水器。潛水器被移動到位置并從主船上解開束縛后部署。MCMS現(xiàn)在希望使用他們的潛水器帶領(lǐng)游客探索愛奧尼亞海底的沉船冒險(xiǎn)。然而，在他們能夠做到這一點(diǎn)之前，他們需要通過開發(fā)安全程序以防潛水器與主船失去通信和可能的機(jī)械故障包括潛水器推進(jìn)力喪失的情況，來贏得監(jiān)管機(jī)構(gòu)的批準(zhǔn)。特別是，他們希望你開發(fā)一個(gè)模型來預(yù)測潛水器隨時(shí)間的位置。不同于陸地上或海面上的典型搜索與救援，有缺陷的潛水器可能會發(fā)現(xiàn)自己位于海底或在水下的某個(gè)中性浮力點(diǎn)。它的位置可能進(jìn)一步受到海流、海水中不同密度和/或海底地理的影響。

你的任務(wù)是：

·定位?- 開發(fā)一個(gè)或多個(gè)模型預(yù)測潛水器隨時(shí)間的位置。

這些預(yù)測有哪些不確定性？

潛水器在事故發(fā)生前可以定期向主船發(fā)送哪些信息以減少這些不確定性？潛水器需要哪些設(shè)備才能做到這一點(diǎn)？

·準(zhǔn)備?- 如果需要，你會推薦公司在主船上攜帶哪些額外的搜索設(shè)備？你可以考慮不同類型的設(shè)備，但也必須考慮這些設(shè)備的可用性、維護(hù)、準(zhǔn)備和使用成本。如果需要，救援船需要帶來什么額外的設(shè)備以協(xié)助？

·搜索?- 開發(fā)一個(gè)模型，使用你的定位模型的信息來推薦初始部署點(diǎn)和搜索模式，以盡量減少定位丟失潛水器的時(shí)間。確定隨時(shí)間和累積搜索結(jié)果找到潛水器的概率。

·推斷?- 你的模型如何擴(kuò)展以考慮其他旅游目的地，如加勒比海？當(dāng)多個(gè)潛水器在同一大致區(qū)域移動時(shí)，你的模型將如何改變？

準(zhǔn)備一份不超過25頁的報(bào)告，提供你的計(jì)劃細(xì)節(jié)。包括一份兩頁的備忘錄，寄給希臘政府，以幫助贏得批準(zhǔn)。

你的PDF解決方案不得超過總共25頁，應(yīng)包括：

一頁摘要。

目錄。

你的完整解決方案。

參考文獻(xiàn)列表。

AI使用報(bào)告（如果使用不計(jì)入25頁限制內(nèi)）。

注意：對于完整的MCM提交沒有具體要求的最小頁數(shù)。你可以使用最多25頁來展示你的解決方案工作和任何你想包含的額外信息（例如：繪圖、圖表、計(jì)算、表格）。接受部分解決方案。我們允許謹(jǐn)慎使用AI，如ChatGPT，盡管不必須通過AI創(chuàng)建解決方案。如果你選擇使用生成式AI，你必須遵循COMAP的AI使用政策。這將導(dǎo)致你必須在PDF解決方案文件的末尾添加一個(gè)額外的AI使用報(bào)告，且不計(jì)入你的解決方案的總頁數(shù)25頁。

術(shù)語表

潛水器：潛水器是一種需要由更大的水上交通工具或平臺運(yùn)輸和支持的水下車輛。這區(qū)分了潛水器和潛艇，后者是自給自足的，能夠在海上進(jìn)行長時(shí)間獨(dú)立操作。

中性浮力發(fā)生在物體的平均密度等于它所浸沒的流體的密度時(shí)，導(dǎo)致浮力與否則會使物體沉沒（如果物體的密度大于它所浸沒的流體的密度）或上升（如果它較輕）的重力平衡。具有中性浮力的物體既不會下沉也不會上升。

MCM/ICM免費(fèi)領(lǐng)真題請掃碼【翰林提供報(bào)名服務(wù)】

Problem B: Searching for Submersibles

Maritime Cruises Mini-Submarines (MCMS), a company based in Greece, builds submersibles capable of carrying humans to the deepest parts of the ocean. A submersible is moved to the location and deployed untethered from a host ship. MCMS now wishes to use their submersible to take tourists on adventures exploring the bottom of the Ionian Sea for sunken shipwrecks. Before they can do this, however, they need to win approval from regulators by developing safety procedures in case of a loss of communication to the host ship and possible mechanical defects including a loss of propulsion of the submersible. In particular, they would like you to develop a model to predict the location of the submersible over time. Unlike in a typical search and rescue on land or on the surface of a sea, the defective submersible could potentially find itself positioned on the sea floor or at some point of?neutral buoyancy?underwater. Its position could further be affected by currents, differing densities in the sea, and/or the geography of the sea floor.

Your tasks are to:

·Locate?- Develop a model(s) that predicts the location of the submersible over time.

What are the uncertainties associated with these predictions?

What information can the submersible periodically send to the host ship to decrease these uncertainties prior to an incident? What kinds of equipment would the submersible need to do so?

·Prepare?- What, if any, additional search equipment would you recommend the company carry on the host ship to deploy if necessary? You may consider different types of equipment but must also consider costs associated with availability, maintenance, readiness, and usage of this equipment. What additional equipment might a rescue vessel need to bring in to assist if necessary?

·Search?- Develop a model that will use information from your location model(s) to recommend initial points of deployment and search patterns for the equipment so as to minimize the time to location of a lost submersible. Determine the probability of finding the submersible as a function of time and accumulated search results.

·Extrapolate?- How might your model be expanded to account for other tourist destinations such as the Caribbean Sea? How will your model change to account for multiple submersibles moving in the same general vicinity? Prepare a report of no more than 25 pages providing the details of your plan. Include a two-page memo of your report addressed to the Greek government to help win approval.

Your PDF solution of no more than 25 total pages should include:

One-page Summary Sheet.

Table of Contents.

Your complete solution.

References list.

AI Use Report (If used does not count toward the 25-page limit.)

Note: There is no specific required minimum page length for a complete MCM submission. You may use up to 25 total pages for all your solution work and any additional information you want to include (for example: drawings, diagrams, calculations, tables). Partial solutions are accepted. We permit the careful use of AI such as ChatGPT, although it is not necessary to create a solution to this problem. If you choose to utilize a generative AI, you must follow the COMAP AI use policy. This will result in an additional AI use report that you must add to the end of your PDF solution file and does not count toward the 25 total page limit for your solution.

Glossary

Submersible: A submersible is an underwater vehicle which needs to be transported and supported by a larger watercraft or platform. This distinguishes submersibles from submarines, which are self-supporting and capable of prolonged independent operation at sea.

Neutral buoyancy occurs when an object's average density is equal to the density of the fluid in which it is immersed, resulting in the buoyant force balancing the force of gravity that would otherwise cause the object to sink (if the body's density is greater than the density of the fluid in which it is immersed) or rise (if it is less). An object that has neutral buoyancy will neither sink nor rise.

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