2015年美国数学建模竞赛第二次模拟赛题

Problem A Warmer Days or Sour Grapes ?The high quality of wines（葡萄酒）produced in the Finger Lakes Region（五指湖区）of upstate （北部）New York is widely known. Proximity（接近）to lakes tempers the climate and makes it more suitable for growing several varieties of premium（独特）grapes: R iesling（雷司令）, G ewürztraminer（琼瑶浆）,C hardonnay（霞多丽）, M erlot（梅洛）, P inot Noir（黑比诺）, and CabernetF ranc（品丽珠）. (There are many more, but we will restrict（限制）the discussion to these six to simplify（简化）the modeling.) Each variety has its own preferred “average temperature” range but is also different in its susceptibility（感受性）to diseases and ability to withstand（抵抗）short periods of unusually cold temperature.As our local climate changes, the relative suitability of these varieties will be changing as well. A forward-looking winery（酒厂）has hired your team to help with the long-term planning. You will need to recommenda) the proportion（比例）of the total vineyard（葡萄园）to be used for growing each of the above six varieties;b) and when should these changes be implemented （实施）(based on observed temperatures and/or current market prices for each type of wine).Naturally, the winery is interested in maximizing its annual profit. But since the latter （后者）is weather-dependent, it might vary a lot year-to-year. You are also asked to evaluate the trade-offs （权衡）between optimizing the expected/average case versus the worst(-realistic-)scenario（情景）.Things to keep in mind:Climate modeling is complicated（复杂）and predicting the rate of “global warming” is a hotly debated area. For the purposes of this problem, assume that the annual average temperature in Ithaca（伊萨卡）, NY will increase by no more than 4°C by the end of this century.It is not all about the average temperature – a short snap（临时）of sub- zero（零度）temperature in late Ferburay or early March (after the vines already started getting used to warmer weather) is far more damaging than the same low temperature would be in the middle of the winter.It takes at least 3 years for a newly planted vine to start producing grapes suitable for winemaking.Problem B Outlook of Car-to-Car TechSAN FRANCISCO -- After more than a decade of research into car-to-car communications, U.S. auto safety regulators took a step forward today by unveiling their plan for requiring cars to have wireless gear that will enable them to warn drivers of danger.These vehicle-to-vehicle (V2V) transmitters and software could save thousands of lives and prevent hundreds of thousands of crashes each year by providing cars with information they never will be able to gather simply from cameras and sensors. “Safety is our top priority, and V2V technology represents the next great advance in saving lives,” Transportation Secretary Anthony Foxx said in an announcement. “This technology could move us from helping people survive crashes to helping them avoid crashes altogether.”Requirement 1: Present a mathematical model to discuss the reduction of the number of traffic accidents and road fatalities/injuries in San Francisco by V2V technology. Requirement 2: Determine the maximum number of cars in San Francisco due to the V2V technology.Requirement 3: Discuss the benefits of V2V technology to alleviate road congestion. Requirement 4: Provide your recommendation to the government.Prblem C Forest FiresOne major environmental concern is the occurrence of forest fires (also called wildfires), which affect forest preservation, bring economical and ecological damage and endanger human lives. Such phenomenon is due to multiple causes (e.g. human negligence and lightnings). Despite an increasing of state expenses to control this disaster, each year millions of forest hectares (ha) are destroyed all around the world.Fast detection is an important element for successful firefighting. Traditional human surveillance is expensive and affected by subjective factors, there has been an emphasis to develop automatic solutions, such as satellite-based, infrared/smoke scanners and local sensors (e.g. meteorological). Propagation models try to describe the future evolution of the forest fire given an initial scenario and certain input parameters. Modeling the dynamical behavior of fire propagation in a forest is helpful for creating scheme to control and fight fire.Requirement 1 Describe several different metrics that could be used to evaluate the effectiveness of fire detection. Could you combine your metrics to make them even more useful for measuring quality?Requirement 2 Model the dynamical behavior of fire spread in a forest. Requirement 3 Discuss the factors to affect fire occurrence. Which factors are the most critical in causing fires. Build mathematical models to predict the burned area of fires using Meteorological Data.Requirement 4 Give y our suggestion for preventing from forest fire and fighting against it.Problem D Wearable Activity RecognitionThe percentage of EU citizens aged 65 years or over is projected to increase from 17.1% in 2008 to 30.0% in 2060. In particular, the number of 65 years old is projected to rise from 84.6 million to 151.5 million, while the number of people aged 80 or over is projected to almost triple from 21.8 million to 61.4 million (EUROSTAT: New European Population projections 2008–2060). It has been calculated that the purely demographic effect of an ageing population will push up health-care spending by between 1% and 2% of the gross domestic product (GDP) of most member states. At first sight this may not appear to be very much when extended over several decades, but on average it would in fact amount to approximately a 25% increase in spending on health care, as a share of GDP, in the next 50 years (European Economy Commission, 2006). The effective incorporation of technology into health-care systems could therefore be decisive in helping to decrease overall public spending on health. One of these emerging health-care systems is daily living physical activity recognition.Daily living physical activity recognition is currently being applied in chronic disease management (Amft & Troter, 2008; Zwartjes, Heida, van Vugt, Geelen, & Veltink, 2010), rehabilitation systems (Sazonov, Fulk, Sazonova, & Schuckers, 2009) and disease prevention (Sazonov, Fulk, Hill, Schutz, & Browning, 2011; Warren et al., 2010), as well as being a personal indicator to health status (Arcelus et al., 2009). One of the principal subjects of the health related applications being mooted is the monitoring of the elderly. For example, falls represent one of the major risks and obstacles to old people’s independence (Najafi, Aminian, Loew, Blanc, & Robert, 2002; Yu, 2008). This risk is increased when some kind of degenerative disease affects them. Most Alzheimer’s patients, for exa mple, spend a long time every day either sitting or lying down since they would otherwise need continuous vigilance and attention to avoid a fall.The registration of daily events, an important task in anticipating and/or detecting anomalous behavior patterns and a primary step towards carrying out proactive management and personalized treatment, is normally poorly accomplished by patients’ families, healthcare units or auxiliary assistants because of limitations in time and resources. Automatic activity-recognition systems could allow us to conduct a completely detailed monitoring and assessment of the individual, thus significantly reducing current human supervision requirements.Most wearable activity recognition systems assume a predefined sensor deployment that remains unchanged during runtime. However, this assumption does not reflect real-life conditions. During the normal use of such systems, users may place the sensors in a position different from the predefined sensor placement. Also, sensors may move from their original location to a different one, due to a loose attachment. Activity recognition systems trained on activity patterns characteristic of a given sensor deployment may likely fail due to sensor displacements.Your task is as follows.(1) Build models to recognize daily living activities.(2) Explore the effects of sensor displacement induced by both the intentionalmisplacement of sensors and self-placement by the user.(3) Verify your recognition models’ toleranc e to sensor displacement.Data Set Information:The REALDISP (REAListic sensor DISPlacement) dataset has been originally collected to investigate the effects of sensor displacement in the activity recognition process in real-world settings. It builds on the concept of ideal-placement, self-placement and induced- displacement. The ideal and mutual-displacement conditions represent extreme displacement variants and thus could represent boundary conditions for recognition algorithms. In contrast, self-placement reflects a users perception of how sensors could be attached, e.g., in a sports or lifestyle application. The dataset includes a wide range of physical activities (warm up, cool down and fitness exercises), sensor modalities (acceleration, rate of turn, magnetic field and quaternions) and participants (17 subjects). Apart from investigating sensor displacement, the dataset lend itself for benchmarking activity recognition techniques in ideal conditions.Dataset summary:#Activities: 33#Sensors: 9#Subjects: 17#Scenarios: 3ACTIVITY SET:A1: WalkingA2: JoggingA3: RunningA4: Jump upA5: Jump front & backA6: Jump sidewaysA7: Jump leg/arms open/closedA8: Jump ropeA9: Trunk twist (arms outstretched)A10: Trunk twist (elbows bent)A11: Waist bends forwardA12: Waist rotationA13: Waist bends (reach foot with opposite hand)A14: Reach heels backwardsA15: Lateral bend (10_ to the left + 10_ to the right)A16: Lateral bend with arm up (10_ to the left + 10_ to the right)A17: Repetitive forward stretchingA18: Upper trunk and lower body opposite twistA19: Lateral elevation of armsA20: Frontal elevation of armsA21: Frontal hand clapsA22: Frontal crossing of armsA23: Shoulders high-amplitude rotationA24: Shoulders low-amplitude rotationA25: Arms inner rotationA26: Knees (alternating) to the breastA27: Heels (alternating) to the backsideA28: Knees bending (crouching)A29: Knees (alternating) bending forwardA30: Rotation on the kneesA31: RowingA32: Elliptical bikeA33: CyclingSENSOR SETUP:Each sensor provides 3D acceleration (accX,accY,accZ), 3D gyro (gyrX,gyrY,gyrZ), 3D magnetic field orientation (magX,magY,magZ) and 4D quaternions (Q1,Q2,Q3,Q4). The sensors are identified according to the body part on which is placed respectively:。