Reference no: EM13371413
A group of students have collected mechanical data (on a MTS machine) from chicken cartilage. Specifically, they have collected data during a stress-relaxation test from 3 samples of femoral and 3 samples of tibial cartilage, and have generated data seen in the figure below.
Their cruel, some might say evil, instructor has asked them to determine if the femoral and tibial cartilage are significantly different by analyzing the data with the following exponential equation.
L(t) = A e-t/T +B
Where L is the load (y-axis), t is time (x-axis) and A, tau and B are parameters that describe the relaxation. To finish their analysis, students will have to determine A, tau, and B for each specimen tested (3 femur + 3 tibia).
Your assignment is to write MATLAB code which will allow these poor helpless students to complete their assignments, by using the lsqcurvefit function.
Specifically you will be create 3 functions and 1 script which will:
1. read in the .dat file (including the header information, you already have this code!), with the added feature of being able to load in a 2nd file but remembering previous file's location.
2. plot load (y-axis) versus time (x-axis), and 'remove' prior to reading the minimum, and 60 seconds AFTER reaching the minimum load.
3. Fit the exponential function to the relaxation data and report the filename as well as the A, tau and B values.
4. Run all 3 functions in sequence to analyze ALL data
function_name - denotes a MATLAB function
PSEUDO-CODE functions:
1. ca02_fun1.m: [data import] - reads data from file, plots result
1.1. INPUT: .dat file name [1xNs string array]
1.2. OUTPUT: data [Ndx3 numeric array], c_labels [1x3 cell array], filename [1xNs]
1.3. look for figure with 'tag' 'relax-test'
1.4. if does not exist, create it, set 'tag' to 'relax-fit', set 'filename' to '*.dat'
1.5. use nargin, if < 1,
1.6. get old file name from 'filename' field
1.7. prompt user for file (uigetfile)
1.8. create new filename
1.9. set 'filename' to dat_filename for figure
1.10. call new function read_datfile
1.11. plot time (x-axis) vs load (y-axis)
1.12. label axes
2. ca02_fun2.m: [data processing/visualization] - find minimum point, and separate relaxation data
2.1. INPUT: data (Ndx3 matrix)
2.2. OUTPUT: data_realx (Nrx3 matrix)
2.3. find row with minimum load value (min)
2.4. determine time at for this row (t_start)
2.5. find last row at t_start + 60;
2.6. create a vector of rows from beginning to end of relaxation data
2.7. export only those rows as variable data_relax
2.8. overlay plot of just the relaxation data
3. ca02_fun3.m: [least square curve fit] - fit an equation to the data and determine the parameters of the exponential
3.1. INPUT: data_relax [Nx3 numeric matrix]
3.2. OUTPUT: fit_parameters [1x3 array]
3.3. lookfor object with 'tag' 'relax-fit' (findobj)
3.4. if you can't find it, create the figure with that 'tag'
3.5. make time your x-data (first remove the initial time point)
3.6. make -1*load your y-data
3.7. create inline exponential function 'x(1)*exp(-x_data/x(2))+x(3)','x','x_data' (this is the function you will be 'fitting'.
3.8. plot time (x-axis) versus load (y-axis)
3.9. initialize x values
3.10. set lower limits
3.11. set upper limits
3.12. run lsqcurvefit get x_fit (fit parameters)
3.13. create an estimate of your y values based on x_fit
3.14. display output in work space (disp)
4. ca02_script.m: [script to run all programs] - this script combines all programs so you can easily analyze many files.
4.1. Outputs from ca02_fun1, are inputs to ca02_fun2
4.2. outputs from ca02_fun2 are inputs for ca02_fun3
4.3. create a 'formatted' output txt with the following fields
4.4. 'filename (stripped of path), A, tau, B