# 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 produced in the Finger Lakes Region of upstate New York is widely known. Proximity to lakes tempers the climate and makes it more suitable for growing several varieties of premium grapes: Riesling, Gewü rztraminer, Chardonnay, Merlot, Pinot Noir, and Cabernet Franc. (There are many more, but we will restrict the discussion to these six to simplify the modeling.) Each variety has its own preferred “average temperature” range but is also different in its susceptibility to diseases and ability to withstand 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 has hired your team to help with the long-term planning. You will need to recommend a) the proportion of the total vineyard to be used for growing each of the above six varieties; b) and when should these changes be implemented (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 is weather-dependent, it might vary a lot year-to-year. You are also asked to evaluate the trade-offs between optimizing the expected/average case versus the worst(-realistic-)scenario. Things to keep in mind: is a hotly debated area. For the purposes of this problem, assume that the annual average temperature in Ithaca, NY will increase by no more than 4° C by the end of this century. average temperature – a short snap of sub-zero 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. suitable for winemaking.

Problem B

Outlook of Car-to-Car Tech

SAN 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 Fires

One 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 against it. Give your suggestion for preventing from forest fire and fighting

Problem D Wearable Activity Recognition
The 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 example, 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 intentional

misplacement of sensors and self-placement by the user. (3) Verify your recognition models’ tolerance 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: 3 --------------------------------------------------------------------------------------------------------------------ACTIVITY SET: A1: Walking A2: Jogging A3: Running A4: Jump up A5: Jump front & back A6: Jump sideways A7: Jump leg/arms open/closed A8: Jump rope A9: Trunk twist (arms outstretched) A10: Trunk twist (elbows bent) A11: Waist bends forward A12: Waist rotation A13: Waist bends (reach foot with opposite hand) A14: Reach heels backwards A15: 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 stretching A18: Upper trunk and lower body opposite twist A19: Lateral elevation of arms A20: Frontal elevation of arms A21: Frontal hand claps A22: Frontal crossing of arms A23: Shoulders high-amplitude rotation A24: Shoulders low-amplitude rotation A25: Arms inner rotation A26: Knees (alternating) to the breast A27: Heels (alternating) to the backside A28: Knees bending (crouching) A29: Knees (alternating) bending forward A30: Rotation on the knees A31: Rowing A32: Elliptical bike A33: Cycling SENSOR 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: S1: left calf (LC) S2: left thigh (LT) S3: right calf (RC) S4: right thigh (RT) S5: back (BACK) S6: left lower arm (LLA) S7: left upper arm (LUA) S8: right lower arm (RLA) S9: right upper arm (RUA) SCENARIOS: The dataset contains information for three different scenarios depending on whether the sensors are positioned on predefined positions or placed by the users themselves. - Ideal-placement or the default scenario. The sensors are positioned by the instructor on predefined locations within each body part. The data stemming from this scenario could be considered as the training set for supervised activity recognition systems. - Self-placement. The user is asked to position a subset of the sensors themselves on the body parts specified by the instructor, but without providing any hint on how the sensors must be exactly placed. This scenario is devised to investigate some of the variability that may occur in the day-to-day usage of an activity recognition system, involving wearable or self-attached

sensors. Normally, the self-placement will lead to on-body sensor setups that differ from the ideal-placement. Nevertheless, this difference may be minimal if the subject places the sensor close to the ideal position. - Induced-displacement. An intentional mispositioning of sensors using rotations and translations with respect to the ideal placement is introduced by the instructor. One of the key interests of including this last scenario is to investigate how the performance of a certain method degrades as the system drifts far from the ideal setup. A complete and illustrated description (including table of activities, sensor setup, etc.) of the dataset is provided in the documentation facilitated along with the dataset.

Attribute Information: The dataset comprises the readings of motion sensors recorded while users executed typical daily activities. The detailed format is described in the package. The attributes correspond to raw sensor readings. There is a total of 120 attributes: Column 1: Timestamp in seconds Column 2: Timestamp in microseconds Column 3-15: [AccX, AccY, AccZ, GyrX, GyrY, Gyr, GyrZ, MagX, MagY, MagZ, Q1, Q2, Q3, Q4] of sensor S1 Column 16-28: [AccX, AccY, AccZ, GyrX, GyrY, Gyr, GyrZ, MagX, MagY, MagZ, Q1, Q2, Q3, Q4] of sensor S2 Column 29-41: [AccX, AccY, AccZ, GyrX, GyrY, Gyr, GyrZ, MagX, MagY, MagZ, Q1, Q2, Q3, Q4] of sensor S3 Column 42-54: [AccX, AccY, AccZ, GyrX, GyrY, Gyr, GyrZ, MagX, MagY, MagZ, Q1, Q2, Q3, Q4] of sensor S4 Column 55-67: [AccX, AccY, AccZ, GyrX, GyrY, Gyr, GyrZ, MagX, MagY, MagZ, Q1, Q2, Q3, Q4] of sensor S5 Column 68-80: [AccX, AccY, AccZ, GyrX, GyrY, Gyr, GyrZ, MagX, MagY, MagZ, Q1, Q2, Q3, Q4] of sensor S6 Column 91-93: [AccX, AccY, AccZ, GyrX, GyrY, Gyr, GyrZ, MagX, MagY, MagZ, Q1, Q2, Q3, Q4] of sensor S7 Column 94-106: [AccX, AccY, AccZ, GyrX, GyrY, Gyr, GyrZ, MagX, MagY, MagZ, Q1, Q2, Q3, Q4] of sensor S8 Column 107-119: [AccX, AccY, AccZ, GyrX, GyrY, Gyr, GyrZ, MagX, MagY, MagZ, Q1, Q2, Q3, Q4] of sensor S9 Column 120: Label (see activity set) Dataset https://archive.ics.uci.edu/ml/machine-learning-databases/00305/

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