All of the needed information is included in the lab document.
UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE & ENGINEERING First Year Program – Core 8 and TrackOne FIRST YEAR PROGRAM ENGINEERING PROBLEM SOLVING LABS MAT188: Laboratory #12 Final Project 0 1 2 3 4 5 6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Time (s) E C G r e c o rd in g Engineering Problem Solving Labs MAT188: Lab #12 Final Project Faculty of Applied Science & Engineering 2 University of Toronto FINAL PROJECT Engineering Problem Solving Using MATLAB In this series of labs you have gained a strong introduction to MATLAB and how it can be used to understand situations and solve problems. You have been introduced to many fundamental functions and commands and these have been summarized in the MATLAB Summary. The purpose of this final project is to review the material presented in the past MATLAB labs and exercises and use your engineering problem solving skills to better understand a real-life scenario. Through this project you will work with on a real-life situation and create a script that will perform simple analysis or computation so that you can draw conclusions from your analysis. Although the suggested examples are chosen to be reasonably straightforward, they demonstrate how engineers face real-world problems and how they use numeric and symbolic computation to help them reach solutions. For this final lab, select ONE PROJECT that is most interesting to you and work towards finding a solution to the problem. Each project must have the following components: 1) Clearly Defined Problem Statement: Each project must have a clear problem statement, which needs to be solved. This doesn’t mean that the problem is such that there is only one “right” answer. 2) Real-World Scenario (Mathematical Model): Each project must be based on a real-world situation, which includes a mathematical model that represents the situation using fundamental scientific principles. 3) Design Parameter: At least one “design” or decision parameter must be included in the problem, such that either the use of for loops and/or conditional statements (e.g., if-elseif- else-end) are a required part of the analysis. 4) Deliverables: The submission for each project must include: a) Script: You will need to create an m-file that generates all the plots and carries out your analysis. It should include every calculation that you do and should include comments throughout your script describing what variables and functions you are using and why. b) Plots: You will need to create at least one two-dimensional plot for your project. Some projects may require multiple plots or three-dimensional plots as well. Plots must be properly labeled (axis and title) and include legend. c) Concluding Statement: You will write a short paragraph that summarizes your analysis and what your suggestion is for a “solution” to the problem. d) A Description of your Engineering Problem Solving Process: You will also submit short descriptions of how you have addressed each of the four key aspects of Pólya’s Problem Solving Process that we have discussed in this course (see details below). Preparation (Required to do before you come to the Lab session) 1. Read through this lab document and the suggested problems below. 2. Choose one of the six suggested problems. Engineering Problem Solving Labs MAT188: Lab #12 Final Project Faculty of Applied Science & Engineering 3 University of Toronto George Pólya’s Problem Solving Process Understanding the Problem What is the unknown? (GOAL) What relevant information is provided? (KNOWNS) What is the condition? What fundamental principles are related? (FOUNDATION) Draw a diagram. (VISUALIZATION) Devising a Plan Consider the unknown. What are the possible connections between the information provided and the unknown. Can the problem be restated in a more useful manner? Do you know a related problem? Can you use its answer or its method? Carrying Out the Plan Check each step as you carry out the plan. Is it leading you in the right direction? Looking Back Can you check the result? How about the solution? Is the answer complete? Have you solved the problem asked? Submission for Final Project You have ONE WEEK (7 DAYS) to complete this assignment, from the date of your lab. As part of this lab, you must submit, your brief descriptions of: 1) Step 1: Understanding the Problem: What is your goal? What relevant information have you been given? What are the fundamental scientific and/or mathematical concepts that you will have to use to solve this problem? Include a simple hand-sketched diagram if it would be helpful. 2) Step 2: Devising a Plan: Without writing or including in your submission ANY MATLAB code, write out your step-by-step process that you plan on using in order to address this problem. This might include: a. The plot or plots you will generate to support your assessment and solution. What do the x and y (or x, y, and z) axes represent? b. The “algorithm”, or step-by-step process you will use in your MATLAB script. This should be written in plain English, no need to use proper or exact MATLAB syntax. If appropriate, include a graphical interpretation (flowchart) for your problem solving process. Please also include any decisions/assumptions that you have made 3) Step 3: Carrying Out Your Plan: What did you do? How did you use MATLAB to solve the problem? This should include: a. The final version of your MATLAB script, b. Any relevant plot or plots that you created to support your assessment, and c. A brief description of ways in which you had to adapt your plan from that which you originally envisioned in Step 2 above. 4) Step 4: Looking Back: How do you know that you have adequately addressed the problem? How are you sure that you have achieved your goal? Is there anything you have learned about the fundamental scientific and mathematical concepts and/or how to use MATLAB for engineering problem solving? Make sure to include a short Concluding Statement that summarizes your analysis and what your suggestion is for a “solution” to the problem. Engineering Problem Solving Labs MAT188: Lab #12 Final Project Faculty of Applied Science & Engineering 4 University of Toronto SUBMISSION GUIDELINES Please submit a single PDF file of maximum 4 pages of text, PLUS your MATLAB files (script, plot, etc.) -- be clear and concise with your writing. Your MATLAB script should run without any adjustments by the user (i.e., the TA). Make sure you test and run your code before submission. Each student works must have an independent submission. Engineering Problem Solving Labs MAT188: Lab #12 Final Project Faculty of Applied Science & Engineering 5 University of Toronto Engineering Problem #1: Analysis of an Annotated ECG Signal Background Electrocardiography (ECG) is the process of recording the electrical activity of the heart over a period of time using electrodes placed on a patient's body. ECG can help the physician in primary diagnosis of different abnormalities in the electrical activity of the heart (arrhythmia). A typical ECG tracing is a repeating cycle of three electrical entities: a P-wave, a QRS complex and a T-wave (see Fig.1). Fig 1. Representation of a normal heartbeat of the human1. Heart beat (rate) measurement is one of the simplest analyses of the heart activity. A heart rate between 60 and 100 beats per minute is considered normal. A heart rate slower than 60 beats per minute is said to be bradycardic and a rate faster than 100 beats per minute is said to be tachycardia. Problem Statement Consider the ECG signals for three patients that have been posted on the course website. These files, ecg1.mat, ecg2.mat, and ecg3.mat contain three columns: time (in seconds), signal voltage (mV), and a marker code. This marker is an annotation of each point by an expert (physician). In this annotation: 0 represents a point with no specific feature in the ECG signal, 1 represents the peak of a P-wave, 2 annotates the Q point, 3 represents the peak of an R-wave, 4 represents a S point, and finally 5 represents a T-wave peak. Analyze these signals so that you can comment on the relative cardiac health of these patients. You may want to focus your analysis on the measures of heartrate and the average PR-interval. You can refer to http://www.ecglibrary.com/norm.php to help you in your assessment. 1 Source: https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/SinusRhythmLabels.svg/2000px- SinusRhythmLabels.svg.png, Accessed November 16, 2017. http://www.ecglibrary.com/norm.php https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/SinusRhythmLabels.svg/2000px-SinusRhythmLabels.svg.png https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/SinusRhythmLabels.svg/2000px-SinusRhythmLabels.svg.png Engineering Problem Solving Labs MAT188: Lab #12 Final Project Faculty of Applied Science & Engineering 6 University of Toronto Engineering Problem #2: Electric Cars Background Electric cars, and plug-in hybrid-electric cars, are becoming more mainstream; the sales of cars like Tesla’s Model 3, Nissan Leaf, Chevrolet Bolt, and other 2018 models have generally increased over the past few years, and are projected to grow over the next decade as well. This case study focuses on the economics of these vehicles as a mode of commuter transportation for those who travel to/from the University of Toronto (return-trip). Please select vehicles from the list here: https://insideevs.com/compare-plug-ins/ It may be necessary to perform additional research (other than the website listed above). Problem Statement • It is possible to determine the before-tax cost, in CAD, for the base model (“lowest cost model”) for each of the four vehicles you’ve selected. • It is possible to use the estimated range of each of these vehicles, as determined by the 2018 Fuel Consumption Guide (NRCAN.gc.ca), in litres/100km. • Use the fuel cost of $105.9 cents/litre for any fuel calculations, if necessary, and variable electricity cost for a 24-hour period beginning 11/26/2018 at 12:00am and ending 11:59pm. Assume a 9am-6pm school day.