Dad-UMD-Projects

Abstract:
This project looks at the number of moves required to make two objects starting at two different places land on the same place in a finite matrix. The matrix consists of two sides, a left and right side. This project focuses on 12 places in the matrix with 7 on the left and 5 on the right. The objects are randomly placed on a position in the left matrix. The objects can move along predetermined paths to meet with the other object. The number of moves required to meet is determined and then through statistical analysis the average expected number of moves can be determined. One rule used in the analysis is that the object cannot return to previous position. The number of moves is defined as the hitting times.
The referenced objects for this object are the mother pig and the piglet. The goal is to get the piglet and mother together on the same position.

Method: (Markov Chain)
Let X0, X1, X2 ….Xn be the piglet random walk, Y0,Y1, Y2, ….Yn be the pig mother random walk
These variables occur independently. Let T=time that the piglet and his mother meet. (Xn = Yn at T=n and Xn <> Ynfor n<T)
In order to easily get this problem started, we choose the case that all holes are connected with each other. When 3 holes are on the left and 4 holes are on the right (Abbr. 3L4R), it is not difficult to find the P(1) is 1/3 and P(2) is 1/6. Once they arrive on the right side, it is equally likely to get to any hole on the left side except the one they had just come from. This property that each hole on one side has the same distribution helps us save a lot of time in finding the other regular patterns. Therefore, we can conclude that if there are N holes on the left and M holes on the right, at specific step n, the probability can be quickly calculated, using the left probability (1-sum of the previous probability) * ((N-2) / (N-1)^2) or ((M-2) / (M-1)^2). The reason for this option in the denominator is the difference between the motion from the left to the right and the right to the left. We noticed that if we combine the motion from the left to the motion from the right and then from right to left, it is a simple loop. So is the motion from right to left to right. By this mathematical method, we found the constant ratio C for P(n+2) / P(n) when n >= 3, which is 1 – (N-2)/(N-1)^2 – (M-2)/(M-1)^2 + (N-2)*(M-2)/(N-1)^2/(M-1)^2. Moreover, after numerous calculations, we were able to find the formula for the expected value to be:
E(T) = P(1) + P(2)*2 + P(3)*(3+2C/(1-C))/(1-C) + P(4)*(4+2C/(1-C))/(1-C),
where P(1) = 1/N, P(2) = (N-1)/N/M, P(3) = (N*M-N-M+1)*(M-2)/M/N/(N-1)^2, P(4) = ((M-1)*(N-1)^3-(N*M-N-M+1)*(N-2))*(M-2)/N/M/(N-1)^2/(M-1)^2, C as shown above.
For the specific 7L5R case, the constant ratio C is 403/576, and the expected value is obtained to be 6.106193231.

To prove that this was true, we wrote the C++ program code and simulate the 7L5R cases with 1 million trials. The program offered us the numbers of meeting time at a certain step. By dividing 1 million, all the probabilities can be obtained. Furthermore, we can get the expected value to be 6.099277.

Given a more realistic model, we assume the piglet can find the mark made by its mother. For this question, it relates to the time that the Markov Chains enter certain sets for the first time. So it still one type of Markov Chain Model. We revised the program and added more codes into it. With the clues each pig leaves, there should be a smaller value for them to get together. Here is the simulation outcome from the second C++ program. It shows that the expected value shorten from 6.099277 to 3.128802, which aligns with our hypothesis

Going back to the project, let N(i) = neighborhood of i, n(i) = number of N(i) = degree of I, and Xi = distribution at step i. It is clearly that X1 ~ DU (7), and X2 ~ (1/7, 1/7, 5/21, 2/7, 4/21). For X3, P(X3=i3) = sum of P(X3=i3, X2=i2, X1=i1) = sum of (1/7 * 1/3 * 1/(n(i)-1)) = 1/7, where i2 N(i3), i1 N(i2) and i1 i3. P(X4=i4) is similar to P(X3=i3) and it is going to be same with P(X2=i2) ~ (1/7, 1/7, 5/21, 2/7, 4/21). So we can conclude that X1 ~ X3 ~ X5 ~X7… and X2 ~ X4 ~X6 ~X8… These same distributions means that there exits two geometric series among all the probabilities, which also were proven by the graph from C++ and excel sheet as shown by the two straight lines with two fixed slopes.

Abstract:
Robotic devices have been widely used in biomaterial processing for many purposes including meat-cutting (deboning) operations for the poultry industry. Tissue is fractured, or removed, from the bone and separated from the bone in these processes. To ensure a high quality product that meets product demand, the cutting force must be precisely controlled in these deboning operations. This research is mainly concentrated on the investigation of the change in cutting force along the cutting path.

Deboning chicken is the example of interest for this paper. Firstly, the microstructures of the blade cutting edges and chicken meat were observed and analyzed. The chicken meat cutting fracture was then explained through the experiments by tensile test and compression test. Secondly, the mechanical properties of chicken meat were determined in a controlled environment. Finally, based on the parameters measured from the micro-scale analysis and material property data generated from tests, the cutting procedure was simulated and analyzed using finite element analysis (FEA) method in an engineering software called ABAQUS. From the results, it was observed that the force at cutting fracture initiation is bigger than the force needed to keep the continuous fracture. It is also observed that the force increases just when the cutting blade moves from a softer material to a harder more dense material like a bone. This jump in the cutting force can be used to indicate the imminent contact between the blade and the bone. Thus, a control algorithm is designed to have an instantaneous response for making certain adjustments for the blade’s position. This research is being done to ensure the chicken breast meat quality by removing all bone chips and maximizing the meat yield before packaging. Furthermore, this system will allow us to provide the basic understanding for the design of force-controlled algorithms that are used in automating robotic cutting of bio-materials in the future.

Introduction
The inline-four cylinder engine is widely used in today’s automobiles. It is an internal combustion engine with four cylinders mounted in a straight line. The pistons are only allowed to be moved in the vertical direction and all of them drive a common crankshaft. By adding force on top of each cylinder face (through combustion), the linear motion is transferred to connecting rods and then to the crankshaft to create rotary motion.

In this CAD project, I will use SolidWorks computer aid design software to make the parts and mate them together as an assembly. Finally, I will use the simulation, motion analysis function to obtain the data we need for this engine.

Slide of video link: https://www.facebook.com/asadjaweddangra/videos/10150246778130342/?t=3

Objective
The purpose of this lab was to analyze the performance of a P.A. Hilton Air Conditioning Laboratory Unit based on experimental data collected once the unit reached steady state operation. In the analysis, common air conditioning assessment and evaluation factors like coefficient of performance and the refrigeration capacity were calculated among other important information.
Summary
In this lab, a P.A. Hilton Air Conditioning Laboratory Unit was analyzed based on the experimental data collected for a dry run with no steam added, and a wet run with steam injected. Once the unit was running at a steady operating state data was collected in specific locations throughout the entire unit. On the air side, the wet-bulb and dry-bulb temperatures were collected at four locations in order to analyze the processes through the air duct. Data was collected in various locations in the refrigeration system to analyze how the vapor-compression refrigeration cycle was performing. Putting these two components of the air conditioning unit together, the performance of the entire unit could be found. Among the topics discussed in this report are the Coefficient of Performance, Energy Efficiency Ratio, Refrigeration Capacity, as well as a discussion in the difference in the wet run and dry run and the physical states of each data location on the air side and refrigeration cycle.
At first glance the measurements that were taken for the wet and dry runs were as expected and none of them stood out to be odd or troubling. This suggested that all of the measurements were realistic and would warrant analysis. The analysis required some assumptions be made because some of the measurements that would be necessary and would be very hard to obtain given the equipment available. An example of these assumptions is the formula used to find the mass flow rate of the dry air. Another assumption made was that there would be no pressure loss through the evaporator or condenser in the refrigeration cycle. Theoretically these assumptions would be adding error to the analysis.
Looking at the Coefficient of Performance (COPR), the wet and dry runs were fairly close to one another. The COPR of the wet run was between 1.993 and 3.188 taking into account the possible range of power consumed by the compressor. The COPR for the dry run was between 1.853 and 2.964, also taking into account the possible range of power consumed by the compressor. It is important to realize that the actual COPR should be somewhere in between these values and most likely in the middle. The Energy Efficiency Ratio (EER) for the dry and wet runs follow pattern because the EER and COPR are related by a constant. Thus, the EER does not add any relative information to the evaluation of the wet and dry runs.
Now comparing the refrigeration capacity, this analysis preformed resulted in a wet run refrigeration capacity of 0.6505 Tons of refrigerant while the dry run had a refrigeration capacity of 0.619 Tons of refrigerant. Based on the COPR calculated and the refrigeration capacities, it would seem that the wet run was slightly more efficient than the dry run. The problem is that the values are fairly close to one another making it possible that it was just a fluke and not a consistent result.

Finally looking at the overall compressor efficiency, the calculations showed that the wet run had an efficiency range of 63% to 102%. The dry run range was from 54% to 87%. Once again this would add to the evidence that the wet run was more efficient than the dry run. But again, these percentages are relatively close. Although the wet run consistently performed slightly better than the dry run, these results should influence a definitive decision that the wet run is more efficient than the dry run because this was only one evaluation. Many more experiments very similar to this one should be done before a decision can be made.

ac_lab_final_edition.pdf
File Size:	3324 kb
File Type:	pdf

Download File

ac-lab-yan_dry-run__final_edition.pdf
File Size:	611 kb
File Type:	pdf

Download File

ac-lab-yan_wet-run__final_edition.pdf
File Size:	707 kb
File Type:	pdf

Download File

thermo_project_final_edition.pdf
File Size:	247 kb
File Type:	pdf

Download File

UMD-HOME | Resume | Photos