Mathematical Modeling

Apart from regular schoolwork, I was also enthusiastic about mathematical modeling. So far, I have signed up for competitions like the 2012 and 2014 Mathematical Contest in Modeling, and have researched on a list of interesting topics, including site selection of hospitals, obstacle avoidance for robots, water security strategy in China, DNA sequencing, the control and eradication strategy of Ebola and others. Among them, I was mostly impressed by the trajectory design of Chang’e 3 and the control strategy of its soft landing, especially for its computer image processing part.

In this project, my team was required to determine the control strategy for Chang’e 3 to land on the moon. Two images of meteor crater on the lunar surface were given to be identified and then we needed to select the flat region for landing, so establishing the rating criteria to evaluate the alternative regions is necessary. For the rough obstacle avoidance, I took variance, range and distance to center point into consideration and utilized different scoring functions to rate these alternatives from each aspect. The region with the highest mark was further divided into sub regions for another round of rating in order to discover the specific target area. While in the phase of accurate obstacle avoidance when stricter standards were set on precision and conditions, I changed the considerations to variance, slope, and distance to center point as well as the weighting on each factor. With a view to reducing the amount of calculation and enhancing the operational efficiency of our program, the location with meteor crater is also needed to be identified.

First of all, I increased the contrast of the original images by means of Logistics Curve so the identification would be easier. Next I applied the Matlab imfill function to fill up the interior zones of the crater. In this way, the area on the image with sparse white dot and concentration of black ones was hence deemed as the flat region. The last step I eliminated these white points with the help of the Matlab strel function and presented the image with white on the major crater regions and black for the flat region, which obviously improved the efficiency of accurate obstacle avoidance algorithm. Finally we rank 3 among over 110 people who participated in Mathematical Contest in Modeling.

Now in retrospect, it’s quite a significant experience for me as I was trying to practice my theoretical learning to solve real problems. Also for my team, we have cooperated for the same aim and knocked over every difficulty. Prior to this, none of us three had got professional experience and gone through systematic training with this regard, but never did we think to retreat in the face of challenges. My team and I buried our heads in the data acquisition and reduction and worked round the clock in modifying our ideas and papers. I savored the pleasure of teamwork by time management, division of labor, as well as team motivation. All of these, for my part, will become great asset for me and be of value in my future study.

You may view all the papers here:

2013 American Mathematical Contest in Modeling Problem B Essay:

2014 National Mathematical Contest in Modeling Problem A Essay:

2015 American Mathematical Contest in Modeling Problem A Essay: