{"id":3560,"date":"2018-09-25T21:18:41","date_gmt":"2018-09-25T11:18:41","guid":{"rendered":"https:\/\/casestudyhelp.com\/sample-questions\/?p=3560"},"modified":"2019-09-19T21:58:55","modified_gmt":"2019-09-19T11:58:55","slug":"matlab-assignments-for-engineering-students","status":"publish","type":"post","link":"https:\/\/casestudyhelp.com\/sample-questions\/matlab-assignments-for-engineering-students\/","title":{"rendered":"MATLAB Assignments for Engineering Students"},"content":{"rendered":"

1.\u00a0 (Worth 100 marks)<\/strong><\/h2>\n

Introduction<\/strong><\/h3>\n

To do something useful with big data, models are devised from the large numbers of observations in order to predict what will occur for some other observation(s). A simple linear model1<\/sup> is of the form:<\/p>\n

\"Formula<\/a><\/p>\n

where y<\/em>i<\/sub><\/em> is the dependent variable, i <\/em>is the observation number (there are a total of M <\/em>observa- tions), x<\/em>ij<\/sub><\/em> is the set of independent variables, N <\/em>is the number of independent variables (for big data, M N <\/em>), and a<\/em>j<\/sub><\/em> are the set of model coefficients. Equation (1) lends itself to a matrix formulation:<\/p>\n

Y <\/strong>= XA<\/strong><\/p>\n

The\u00a0 model\u00a0 coefficients\u00a0 a<\/em>j<\/sub><\/em>\u00a0 <\/em>are\u00a0 determined\u00a0 by\u00a0 measuring\u00a0 y<\/em>i<\/sub><\/em>\u00a0 <\/em>and\u00a0 x<\/em>ij<\/sub><\/em>.\u00a0\u00a0 One of\u00a0 the\u00a0 dangers of developing such a model is \u201cover-fitting\u201d the data. This is where a<\/em>j<\/sub><\/em> are tuned for the M <\/em>observations so that a<\/em>j<\/sub><\/em> is an excellent model for y<\/em>i<\/sub><\/em>, <\/em>i <\/em>\u2264 <\/em>M <\/em>, but is a poor model for y<\/em>i<\/sub><\/em>, <\/em>i > M <\/em>.\u00a0 Good practice is therefore to split the M <\/em>observations into a \u201ctraining dataset\u201d (with M<\/em>1<\/sub> observations,\u00a0 M<\/em>1<\/sub> \u2265 <\/em>N\u00a0 <\/em>and\u00a0 typically\u00a0 M<\/em>1<\/sub>\u00a0\u00a0\u00a0 N <\/em>) and\u00a0 a\u00a0 \u201ctest\u00a0 dataset\u201d\u00a0 (with\u00a0 M<\/em>2<\/sub> observations, M<\/em>1<\/sub> + M<\/em>2<\/sub> = M <\/em>, and typically M<\/em>2<\/sub> < M<\/em>1<\/sub>). The\u00a0 values\u00a0 of\u00a0 a<\/em>j<\/sub><\/em> are\u00a0 determined\u00a0 from\u00a0 Eq.\u00a0 (1)\u00a0 using the training dataset (with M<\/em>1<\/sub> observations). The values can then be validated using the test dataset by calculating y<\/em>i<\/sub><\/em> using Eq. (1) and calculating the error from the actual values y<\/em>\u02c6i<\/sub><\/em>.<\/p>\n

In this question, you are going to apply this methodology to determine if it is possible to estimate the mean pressure for the year based on temperature readings from each month. The ideal gas law is:<\/p>\n

p <\/em>= \u03c1RT<\/em><\/strong><\/p>\n

where p <\/em>is the pressure, \u03c1 <\/em>is the density, R <\/em>the ideal gas constant and T <\/em>the temperature.<\/p>\n

Your computational task is to use Eq. (1)<\/p>\n

\"Formula<\/a><\/p>\n

in the form of Eq. (2)<\/p>\n

P <\/strong>= TA<\/strong><\/p>\n

for \u00a0the \u00a09:00 \u00a0readings.\u00a0 \u00a0Here \u00a0p<\/em>\u00afi<\/sub><\/em> is \u00a0the \u00a0average \u00a0pressure \u00a0across \u00a0all \u00a0months \u00a0for \u00a0day \u00a0i<\/em>, \u00a0T<\/em>ij<\/sub><\/em> is \u00a0the temperature on day i <\/em>and month j\u00a0 <\/em>and a<\/em>j<\/sub><\/em> is the average coefficient for month j<\/em>.\u00a0 You\u00a0 will use\u00a0 the entire 12 months\u2019 worth of data (N\u00a0 <\/em>= 12) to calculate the average pressure for each calendar\u00a0 date (M<\/em>\u00a0 <\/em>= 28 since there are only 28 days in February), i.e. p<\/em>\u00af1<\/sub> is the average pressure calculated using the 1st of July, 1st of August, 1st of September, etc. For your assignment, the following value is to be used:<\/p>\n

\"Formula<\/a><\/p>\n

where M<\/em>2<\/sub> is to be rounded to the nearest integer. Because M > N <\/em>(we don\u2019t have M N <\/em>), we will work with M<\/em>2<\/sub> \u2264 <\/em>N <\/em>, which is not ideal, but is pragmatic, since it guarantees that M<\/em>1<\/sub> > N\u00a0 \u00a0<\/em>to produce statistically-good estimates of a<\/em>j<\/sub><\/em>.<\/p>\n

Requirements<\/h3>\n

For this assessment item, you must perform hand calculations using Eq. (5):<\/p>\n

    \n
  1. Calculate a<\/em>1<\/sub> using only the 1st of July (i.e. M <\/em>= 1, N <\/em>= 1).<\/li>\n
  2. Calculate a<\/em>1<\/sub> and a<\/em>2<\/sub> using only the 1st and 2nd of both July and August (i.e. M <\/em>= 2,\u00a0N <\/em>= 2).<\/li>\n<\/ol>\n

    You must also produce MATLAB code which uses Eq. (5):<\/p>\n

      \n
    1. Repeats Requirements 1 and 2. Reports and verifies the<\/li>\n
    2. *Successfully loads all the relevant<\/li>\n
    3. *Repeats Requirement 2 using the loaded data. Reports and verifies the<\/li>\n
    4. **Reports the value of M<\/em>2<\/sub> before it is rounded, to confirm the values of M<\/em>1<\/sub> and M<\/em>2<\/sub> you are to use. Calculates all the a<\/em>j<\/sub><\/em> using the training dataset of M<\/em>1<\/sub> values and reports a<\/em>j<\/sub><\/em>.<\/li>\n
    5. **Uses the test dataset of M<\/em>2<\/sub> values to assess the quality of the modeled values of p<\/em>\u00afj<\/sub><\/em>.<\/li>\n
    6. ***The accuracy of the results is limited because the variability in the temperature\u00a0 and pressure data is\u00a0 in\u00a0 the\u00a0 3rd\u00a0 or\u00a0 4th\u00a0 significant\u00a0 figure,\u00a0 and\u00a0 also\u00a0 because\u00a0 we\u00a0 do\u00a0 not\u00a0 have big data. To remedy\u00a0 the\u00a0 problem\u00a0 of\u00a0 significant\u00a0 figures,\u00a0 the\u00a0 data\u00a0 should\u00a0 be\u00a0 The first normalization technique to use in this circumstance is to \u201ccentre\u201d the data in\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the matrix T <\/strong>(subtract a constant\u00a0 value,\u00a0 sometimes\u00a0 the\u00a0 mean,\u00a0 from\u00a0 all\u00a0 the\u00a0 data),\u00a0 which\u00a0 will make the variability in the 1st or 2nd significant figure. Use 15\u25e6<\/sup><\/em>C to centre\u00a0 the\u00a0 temperature data, produce\u00a0 new\u00a0 a<\/em>j<\/sub><\/em>\u00a0 <\/em>from\u00a0 your\u00a0 training\u00a0 dataset\u00a0 and\u00a0 test\u00a0 the\u00a0 coefficients.\u00a0 See if you achieve some further numerical improvement in this case by\u00a0 \u201cscaling\u201d the data\u00a0\u00a0 in T <\/strong>(non-dimensional sing, normally\u00a0 by dividing\u00a0 by\u00a0 the\u00a0 standard\u00a0 deviation)\u00a0 so\u00a0 that\u00a0 all\u00a0 the quantities are of the same order of magnitude2<\/sup>.<\/li>\n
    7. Discusses the<\/li>\n
    8. Have appropriate comments<\/li>\n<\/ol>\n

      The projected difficulty of a Requirement is indicated by the number of * at the start. All students are expected to be able to complete Requirements which do not have an *.<\/p>\n

      Assessment Criteria<\/h2>\n

      Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method\/code will receive full marks.<\/p>\n

      \"table\"<\/a>
      \n<\/a><\/p>\n

      2.\u00a0 (Worth 100 marks)<\/h2>\n

      Introduction<\/h3>\n

      When data is being measured, it is common for there to be data missing, which could be due to a fault in the measuring equipment, or the variable being unmeasurable at that moment. In the weather data for Dalby, the maximum temperature was not recorded on 29th October 2017, presumably because not all the temperature readings were recorded for that day, so therefore it is impossible to know whether the highest recorded temperature was actually the maximum. Leaving unknown\/unreliable readings blank is the best option, since inserting a value (such as zero) could be a valid value, and therefore pollutes the data (this is why my preferred option is to fill an empty slot in an array with NaN, since it is unlikely to have occurred from a calculation). If you need to be able to use a value where there is one missing, then you need to use some method of including an intelligent guess. In this question, you will use a global curve-fit to provide the guess. All of you will use T<\/em>3<\/sub> (the temperature measured at 3:00 pm) as the independent variable to model the maximum daily temperature, T<\/em>max<\/sub>. You will also compare the outcome for this modelling to using another variable, V <\/em>, as the independent variable. For Your assignment, the following value is to be used:<\/p>\n

      Q<\/em>2<\/sub> = 4.<\/em>1501 .<\/em><\/strong><\/p>\n

      The independent variable (besides T<\/em>3<\/sub>) you are to use is based on your value of Q<\/em>2<\/sub>:<\/p>\n

      V <\/em>\u2261 <\/em>T<\/em>min<\/sub> ,\u00a0 Q<\/em>2<\/sub> \u2264 <\/em>5<\/strong><\/p>\n

      V\u00a0 <\/em>\u2261 <\/em>T<\/em>9<\/sub> ,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Q<\/em>2<\/sub> > <\/em>5<\/strong><\/p>\n

      where T <\/em>is temperature and the subscript refers to either the daily minimum or the particular time of day.<\/p>\n

      Your\u00a0 task is to estimate the value\u00a0 of T<\/em>max<\/sub> on 29th October 2017 using both T<\/em>3<\/sub> and V <\/em>as\u00a0\u00a0 the independent variable.<\/p>\n

      Requirements<\/h2>\n

      For this assessment item, you must perform hand calculations using T<\/em>max<\/sub> and T<\/em>3<\/sub>:<\/p>\n

        \n
      1. Take the values from 28th and 30th October 2017 and estimate the coefficients of the three standard curve-fitting functions. These data points will provide a qualitative repre- sensation of the overall<\/li>\n<\/ol>\n

        You must also produce MATLAB code which:<\/p>\n

          \n
        1. Repeats Requirement 1 and verifies the<\/li>\n
        2. *Performs curve-fits of all the data for T<\/em>max<\/sub> and T<\/em>3<\/sub>. Use the MATLAB function isfinite to filter the dataset so that only those dates with recordings of both T<\/em>max<\/sub> and T<\/em>3<\/sub> are included.<\/li>\n
        3. Validates the three standard curve-fitting functions obtained in Requirement 3\u00a0 by\u00a0 com-\u00a0 paring with the parameters obtained in Requirement 1. Given the limited data used in Requirement 1 and the overall scatter in data, don\u2019t expect the values to be very<\/li>\n
        4. Determines which curve-fit is the<\/li>\n
        5. Demonstrates that the chosen curve-fit is the best both graphically and numerically, show- ing both the data and the relevant curve-fit.<\/li>\n<\/ol>\n
            \n
          1. Displays a message in the Command Window stating which type of curve-fit was chosen, stating the parameters of the curve-fit and the result of the numerical test of the curve-fit.<\/li>\n
          2. Plots the best curve-fit along with the data in a separate figure with normal-scale<\/li>\n
          3. Uses the best curve-fit to estimate T<\/em>max<\/sub> for 29th October<\/li>\n
          4. *Reports the value of Q<\/em>2<\/sub>, leading to the selection of V <\/em>. Repeats Requirements 3, 8 and 9 using only a linear curve-fit with V <\/em>the independent variable instead of T<\/em>3<\/sub>. Plots the curve-fit along with the Compares and discusses the two estimates for T<\/em>max<\/sub>.<\/li>\n
          5. Have appropriate comments<\/li>\n<\/ol>\n

            The projected difficulty of a Requirement is indicated by the number of * at the start. All students are expected to be able to complete Requirements which do not have an *.<\/p>\n

            Assessment Criteria<\/h2>\n

            Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method\/code will receive full marks.<\/p>\n

            \"table<\/a><\/p>\n

            3\u00a0 (Worth 100 marks)<\/h2>\n

            Introduction<\/h3>\n

            This question provides an alternative methodology to the problem in Question 2. In this question, you will use interpolation to provide the guess. Time is an obvious independent variable to use, but Question 2 suggests that there are other options. For your assignment, the following value is to be used:<\/p>\n

            Q<\/em>3<\/sub> = 2.<\/em>4937 .<\/em><\/strong><\/p>\n

            The independent variable (besides time), V <\/em>, you are to use is based on your value of Q<\/em>3<\/sub>:<\/p>\n

            V <\/em>\u2261 <\/em>T<\/em>min<\/sub> ,\u00a0 Q<\/em>3<\/sub> \u2264 <\/em>5<\/strong><\/p>\n

            V\u00a0 <\/em>\u2261 <\/em>T<\/em>3<\/sub> ,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Q<\/em>3<\/sub> > <\/em>5<\/strong><\/p>\n

            Where T <\/em>is temperature and the subscript refers to either the daily minimum or the particular time of day.<\/p>\n

            Your task is to estimate the value of T<\/em>max<\/sub> on 29th October 2017 using these two independent variables. For this problem you are to only use data from 19th to 31st October inclusive (a total of 12 days not including 29th October). These dates have been chosen to ensure that you do not have repeated values of the independent variable (which is numerically problematic) and also that you have sufficient data either side of 29th October for the interpolation methods to be numerically reliable.<\/p>\n

            Requirements<\/h2>\n

            For this assessment item, you must perform hand calculations:<\/p>\n

              \n
            1. Estimate the maximum temperature on 29th October 2017 using linear interpolation with time the independent<\/li>\n
            2. **Repeat Requirement 1 using V <\/em>as the independent variable. You must also produce MATLAB code which:<\/li>\n
            3. Repeats Requirements 1, reporting the result to the Command<\/li>\n
            4. Verifies Requirement<\/li>\n
            5. Repeats Requirement 1 using cubic splines. Additionally validates the result with Re- quirement<\/li>\n
            6. ***Reports the value of Q<\/em>3<\/sub>, leading to the selection of V <\/em>. Repeats the calculations of Requirements 3\u20135 using V <\/em>as the independent variable. The results using the cubic spline method will not be very good for one reason or another. The function sortrows<\/li>\n
            7. Compares and discusses the 2 answers for T<\/em>max<\/sub> on 29th October 2017 from Question 2 and the 4 answers from this<\/li>\n
            8. Has an appropriate comment<\/li>\n<\/ol>\n

              Assessment Criteria<\/h3>\n

              Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method\/code will receive full marks.<\/p>\n

              \"table<\/a><\/p>\n

              4.\u00a0 (Worth 100 marks)<\/h2>\n

              Introduction<\/h3>\n

              Predicting what will occur is the essence of a model. Many people rely on weather forecasting for their livelihood, and many more people for their ordinary lives. Your task is to devise and construct a simple model for two of the variables in the Bureau of Meteorology dataset: the temperature at 3:00 pm (T<\/em>3<\/sub>) and the relative humidity at 9:00 am (\u03c6<\/em>9<\/sub>).<\/p>\n

              To obtain consistent results from your random number generation, you should initialise the seed to a fixed value using rng(seed). For your assignment, the value is:<\/p>\n

              seed = 1.<\/em>1259<\/strong><\/p>\n

              Requirements<\/h2>\n

              For this assessment item, you must perform hand calculations on the data for July:<\/p>\n

                \n
              1. Calculate the sample mean and standard deviation for T<\/em>3<\/sub> and \u03c6<\/em>9<\/sub> for the first 10 data values of each<\/li>\n
              2. Use the first 20 data values T<\/em>3<\/sub> and \u03c6<\/em>9<\/sub> to estimate the sample pdf (i.e. the scaled frequency). Plot the sample pdfs. You can produce the plots in MATLAB, but you must perform the calculations of the value of the pdf for each value of T<\/em>3<\/sub> or \u03c6<\/em>9<\/sub> by<\/li>\n<\/ol>\n

                You must also produce MATLAB code which:<\/p>\n

                  \n
                1. Repeats the hand calculations and verifies the MATLAB<\/li>\n
                2. Loads the entire 12 months\u2019 worth of data. The rest of the analysis is to be on the full dataset in this file3<\/sup>.<\/li>\n
                3. *One of T<\/em>3<\/sub> and \u03c6<\/em>9<\/sub> can be represented by a standard distribution. Determine which variable and the corresponding distribution which best describes the variable, including proof that this distribution is an appropriate model and proof that the other variable cannot be modelled by the same distribution. Part of this proof may be demonstrated by completing Requirements 6\u20138.<\/li>\n
                4. *Calculates the parameters of the population distribution for both variables, including the associated error in the estimation of the parameters. Reports the values to the Command Window.<\/li>\n
                5. *Calculates the sample mean and sample standard deviation for both variables, along with an assessment of the accuracy of these<\/li>\n
                6. *Graphically compares the sample pdf and population pdf for both<\/li>\n
                7. *Reports to the Command Window a discussion of the applicability of the population distribution for both<\/li>\n
                8. **Performs modelling for only the chosen variable from Requirement 5. Produces a prediction of the values for the 12 months by randomly generating samples from the distribution. Plots the time series of values which is thus produced along with the history of the recorded values. Discusses the validity of the predicted values in predicting the actual history (some analysis will assist you in drawing conclusions).<\/li>\n
                9. Has an appropriate comment<\/li>\n<\/ol>\n

                  Assessment Criteria<\/h3>\n

                  Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method\/code will receive full marks.<\/p>\n

                  \"table<\/a><\/p>\n

                  Submission<\/h3>\n

                  Submit your code, with the *.csv files that are provided to you, by the due date to the Study- Desk. Submit your hand calculations as a pdf file. Note that:<\/p>\n

                    \n
                  • You do not need to rename your files when uploading: the system automatically segregates different students\u2019<\/li>\n
                  • If you can see that the files have uploaded, then you have successfully submitted your assignment. There is no need to click a \u201csend for marking\u201d button, but you will have to click a button confirming that the submission is your own<\/li>\n
                  • You MUST <\/strong>upload all of your code along with input\/output files in a *.zip file. The following are the only file types that can be submitted:\n
                      \n
                    • *.zip<\/li>\n
                    • *.pdf<\/li>\n
                    • *.doc<\/li>\n
                    • *.docx<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                      The system will block any attempt by you to upload a file which doesn\u2019t match any of those file extensions.<\/p>\n

                        \n
                      • If you forgot to submit a file, do not upload it after the due date:\u00a0 the submission time\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 is based on when the last file was You should email the examiner in this circumstance (with any file attached). If you remember close to midnight on the day you made your submission, you only need to upload the file (don\u2019t bother emailing), since the submission day will effectively be the same.<\/li>\n<\/ul>\n