Lecture 4: Data Visualization

B Burlingame

23 Sept 2015

Announcements

Homework 2 due next week Lab 3 due in Lab Still no canvas access

The Plan for Today

Data visualization for engineering applications Charting and data presentation Example: LVDT calibration Adding a trend line to data Spark lines Using spreadsheet data with MatLab

Graphical Presentation in Engineering

Presenting data in graphical form is extremely important! A picture really is worth a thousand words!

Especially for engineering!

Excel & Matlab offer very powerful, easy to use graphical presentation tools.

Prose vs. a Figure

Tube wall and reflector pin temperatures vs. time during the radiative heating

feasibility test.The focus of the concentrator was brought into axial alignment with the tube bore at about t=1.4 s and re-adjusted at about t=5 s. The radiant flux impinging on the bore of the tube was estimated to be about 1.65 MW/m^2 from measurements made after the test. The tube wall temperature rises rapidly to about 275 ºC in comparison to the reflector pin, confirming predictions that non-contact heating using a radiant source and an internal conical reflector is indeed feasible.

Which would you rather look at?

Or

LVDT Sensor Linear Variable

Differential Transformer non-contact, friction-free

position sensor infinite resolution absolute position

measurement robust

Need to calibrate Measure output voltage

as the core is moved known amounts

Plot voltage vs. displacement

http://www.transtekinc.com/assets/images/240ACTION.gif

http://www.macrosensors.com/images/tutorial_page_images/images/fig1.jpg

http://www.rdpe.com/us/hiw-lvdt.htm

LVDT application – Road Simulator

http://www.swenox.com/gtc/images/4-axis-durability-rig.jpg

Calibration of LVDT Sensor

Method used by Leroy-Crandall Geotechnical Laboratory

http://gees.usc.edu/soilab/Photos/Calibration%20Pictures/mvc-159f.jpg

http://gees.usc.edu/soilab/Calibration.htm

Micrometer head

LVDT core

LVDT body

core motion

Formatting Your Chart Default is probably not the best! Publication or presentation?

Publication No fill of chart background No fill of data point markers B&W markers, lines, annotation Use line types that can be differentiated in a B&W photocopy Maximize chart area For landscape orientation, title goes closest to the spine

Annotate well Descriptive title Labeled axes with units!! Error bars with measured data

Creating a Figure

Maximize the information transfer What will the busy (or lazy) reader actually

read of your report? Structure of figure annotation:

Figure number Figure title Figure caption

Really important and often overlooked!

Figure number must be

referred to in the report

Figure title Descriptive

Figure caption The key

information you want the reader to understand from the figure

Note inset figure and additional annotation for clarity

Figure Example

(Furman, 1991)

Tube wall and reflector pin temperatures vs. time during the radiative heating feasibility test

XY Scatter vs. Line Chart

What is the difference? Different treatment of the x-axis data

XY Scatter Chart: for x data that varies continuously Interpolating between points makes sense Ex. temperature vs. time over 24 hrs

Line Chart: for x data that is categorical or equally spaced Interpolating between points may not make sense Ex. average lab report score for Tues, Wed, Thurs sections

XY Scatter Charto x-axis data varies continuouslyo Actual x-axis data that is unequally

spaced will be plotted properlyo good for analyzing trend in datao most often used for engineering

analysis

Line Charto x-axis data will be equally spaced on

the chart (beware!). If the actual x data is not equally spaced, the plot will be misleading.

XY Scatter vs. Line Chart, cont.

Smoothed line or not? Generally, not

Smoothed line can be misleading unless generating function is a good representation of actual behavior of the data

Better to leave as points or fit a regression line/curve that is a likely candidate to describe the underlying behavior

right-click | Format Data Series | smoothed line check-box

Adding Data Series

Cases where you might have additional data to add to a chart Calculations on a data set Multiple data sets

Right-click in the plot region ‘Select Data’ (2007) or ‘Source data’ (2003) Add a data series

Name X values Y values If x values are the same as previous, can just cut-and-paste

Example: LVDT_dataset_for_lecture.txt

Plotting in MatLab

There are many plot types in MatLab as well

X-Y in Excel == plot() Basic: plot(x,y) General: plot(x1,y1,…,xn,yn)

Formatting: xlabel, ylabel, title, legend

Calculating Linear Approximation Use polyfit to find the slope and intercept

Recall slope-intercept form of a linear equation y = mx + b (m = slope, b = x-intercept)

polyfit(x,y,1) The first value is the slope, the second the

intercept Given: A = polyfit(x, y, 1) linearY = x .* A(1) + A(2) plot(x, linearY)

Plots the linear approximation

Adding a Secondary Y-axis

Sometimes it is useful to plot multiple data sets on the same graph that have the same x-values, but vastly different y-values.

Plotting with multiple axis in MatLab

Basic: plotyy(x1,y1,x2,y2) – Must share the same X scale

General: line & label Complicated. The tutorial is here: http://

www.mathworks.com/help/matlab/creating_plots/using-multiple-x-and-y-axes.html

Sparklines

A small, high resolution graphics embedded in a context of words, numbers, images – Edward Tufte [2004]

Ex: 1979 saw a general upward trend in the price of gasoline . There are some commentators who believe spiraling energy costs directly lead to Jimmy Carter’s loss in the 1980 election.

Numerical Integration

Trapezoidal integration Ex. area under a

curve

Area Under ( 3+2cos(px/10) )

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

)10

cos(23 xyp

Numerical Integration, cont. Divide into trapezoids Calculate the area of the

trapezoids

Sum areas Voila! Results

Exact 21.3661977

Numerical 21.3137515

)(2 1

1ii

iii xx

yyA

Numerical Integration (recap)

Can think of integration as finding the area under a curve Break area

up into trapezoids

http://people.oregonstate.edu/~haggertr/487/integrate.htm

Numerical Integration Example

http://www.onid.orst.edu/~haggertr/487/integrate.xls

Numerical Intergration – Matlab Built in command

trapz(X, Y) X == the horizontal spacing Y == vertical magnitudes at each X

Example – Integral of Sine from 0 - π X = 0:pi/100:pi;

recall, returns 100 values from 0 to pi Y = sin(X); Q = trapz(X, Y);

Q will now hold 2, the integral of sine from 0 to pi

Numerical Differentiation

(Larsen, 2009)

First derivatives

Numerical Differentiation, cont.

Second derivatives

(Larsen, 2009)

References Furman, B. (June, 1991). A new, thermally controlled,

non-contact rotor balancing method (Doctoral dissertation). Available from University Microfilms International (UMI No. 9205634). p. 227

Larsen, R. W. (2009). Engineering with Excel, Pearson Prentice Hall, New Jersey. ISBN 0-13-601775-4

Engineering with Excel companion website: http://www.chbe.montana.edu/excel/EngExcel3.htm. Visited 25OCT2009.

Edward Tufte forum: Sparkline theory and practice Edward Tufte. Website: http://www.edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=0001OR.