Transcript Introduction to Modeling Working with Data - CMA

Technology Enhanced
Inquiry Based Science Education
Working with data in Coach
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Data Table
• One Data Table with all variables and their data
per activity.
• The variables are created automatically based
on Sensor, Video measurement or Model data.
• Variables for manual data or data calculated by
formulas can be added.
• No limitation in the number of variables used in
the table but for better visibility variables (table
columns) can be hidden.
• More measurement runs possible.
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Data Table
Data Series
Run Series
Variables can be added as well to the left as to the right side of the Data Table.
This allows adding a parameter (one value per Run) into Run Series or
a new calculated quantity into Data Series (this quantity will be calculated, if
possible, for all Runs in the Table).
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Using formulas
It is possible to do
calculations on the data by
using formulas (arithmetical
operators, mathematical
and special functions).
During a new run, the newly
calculated values appear
in real-time.
Example: measuring p and V,
and creating a diagram of
V vs. 1/p (Boyle’s law).
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Graphs
• Many graphs possible
• Standard graphs are created automatically via
right-click on a sensor icon or on a model
variable.
• User-defined
graphs are created
very quickly via
dragging variable
labels from the
Data Table.
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Data Analysis and Processing
• Once data is collected, you need tools to
analyse or process the data.
• Data analysis usually refers to getting
information from the data, for instance by
looking in more detail (zooming), reading coordinates of points in the graph, or determine a
slope of a tangent line to the graph.
• Data processing means that the data are
worked in one way or another to produce new
data.
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Overview of tools
Analysis
• Zoom
• Scan
• Slope
• Area
• Statistics
Processing
• Select/Remove data
• Smooth
• Function fit
• Derivative
• Integral
• Signal Analysis
• Histogram
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Zoom
To see the data in
more detail the Zoom
function can be used.
An area of the graph
will be enlarged for
closer inspection.
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Scan
To read the co-ordinates of points on graphs use the option
Scan can be used. The co-ordinates are displayed in the box.
Example: scanning a position vs. time graph.
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Slope
Slope gives the slope of
the tangent at any point
of a displayed graph.
This is a measure of the
rate with which a quantity
changes, e.g. the speed
of an object.
Example: the rate at
which a capacitor
discharges at t=0,29s.
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Area
With Area the area
between a displayed
graph, the horizontal axis
and two boundary lines,
can determined.
Example: area under the
graph of an induced
EMF by a falling magnet.
The area is a measure of
the magnetic flux B.
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Statistics
Use the Statistics
option to display
statistical information
about the variable
values of a selected
run.
Example:
statistical data from a
data set of the mean
height of Dutch boys
(green graph) and girls
(red graph) from age 1
to 21.
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Select/Remove data
Use the Select/Remove Data option to reduce the
number of points in a run. A range of data (e.g. if part of
the data is irrelevant) or single points (e.g. if your data set
has spikes - erroneous measurements) can be selected
from the graph for removal or retention.
Example Range: cutting off
the first horizontal part of a
graph recorded during
discharging of a capacitor.
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Select/Remove data
Example Points: selecting
points for analyzing the
function which describes the
envelope of damping
oscillations.
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Smooth
Use the Smooth option to create a smooth curve
that fits (interpolates) a rough or limited number
of points.
This option offers three techniques of
approximations:
• Moving average,
• Bezier, and
• Spline.
The smoothed graph may consist of (much) more
points than the original data set and can
successively be processed.
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Smooth: Moving average
Use Moving average to reduce noise and eliminate
fluctuations in the graph. The smoothed graph has the same
number of points and each point is replaced by the average
of a number of neighbouring points.
The Filter width parameter
determines this number of
points.
Moving average is often used Original graph Filter width = 1 Filter width = 2
to highlight long-term trends
and cycles.
Example: CO2-measurement,
Filter width determines the
degree of filtering.
Original graph
Filter width = 1 Filter width = 10
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Smooth: Bézier
Use Bezier to create
a smooth curve with
more points then the
original data set.
The smoothed graph is
forced through the first
and the last original
point. The intermediate
points determine the
degree of curvature of
the smooth graph.
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Smooth: Spline
Use Spline to smooth a graph by means
of a polynomial approximation of 5th
degree. A smoothing factor controls the
trade off between fitting the raw data
and minimizing the roughness of the
approximation.
For a lower value of smoothing factor
the spline curve gets closer to the raw
data. When its value is 0 the smoothing
curve is a natural quintic spline curve
through all original points.
Spline is a powerful tool to deal with
noisy data and for computation of
smooth derivatives.
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…..….
Smoothing factor of resp.
0, 0.05, 5.154 (auto) and 10,000.
Function fit
For verifying data against theory
one usually wants to approximate
the data with a standard
mathematical function.
Function fit is a procedure to
make such approximation.
A large number of standard
mathematical functions are
available.
The coefficients of the fit function
are determined using a leastsquares method.
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Function fit: linear fit
Position vs. time
data of a motion of
a cart moving away
from the sensor.
A linear fit on the
straight part of the
graph gives the
velocity during this
phase of the motion
(v=-0.15 m/s).
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Function fit: quadratic fit
The best (quadratic)
fit of the vertical
position data from a
video measurement
of a basketball shot.
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Function fit: exponential fit
The process of discharging
of a capacitor can be
described by an
exponential function.
The coefficient ‘a’ of the
fit-function is related to
the begin voltage of the
capacitor, while ‘b’ is
related to the ‘RC-time’,
the time interval it takes to
reach half of the begin
voltage of the capacitor.
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Derivative
Derivatives are very important in science, as they are a measure of
the rate of change of a quantity. They are used often to calculate the
speed of processes, or the point where change is maximum.
Differences method:
direct calculation via differences
between successive points
(often noisy).
Smooth method: the derivative
is applied to a smooth spline
function from the data.
Example: determining the velocity
(red graph) from the position
graph (blue graph).
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Integral
The Integral option is used to calculate the function (the primitive
function) whose derivative is equal to the displayed graph. Such an
integral function can be determined but for a constant - the constant of
integration.
Example: obtaining the
volume-time graph by
integrating over time
a spirogram, a measurement
of human breathing with
a spirometer.
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Signal Analysis
If you have a sound signal consisting of a
number of frequencies, e.g. a tone of a musical
instrument, or a spoken or sung vowel,
Signal Analysis can help you to analyse which
frequencies are present or, in case of speech,
which formants are present in the signal.
There are four methods:
• Fourier Transform
• Linear Prediction
• R-ESPRIT
• Prony.
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Signal Analysis of sound beats
Original waveform
Prony
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Fourier transform
R-Esprit
Signal Analysis: Linear Prediction
Linear Prediction (LP) is
suitable for analysing sound
vibrations of the human voice.
Example: two spectra from
the vowel ‘a’ (as in ‘Cake’)
sung one fifth apart (same
male voice). The overall
shape of the graphs share
some characteristics resulting
from resonances from the
shape and cavities of the
singer.
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Histogram
With Histogram you can
get a graphical
representation of the
distribution of your data.
It indicates the number
of data points that lie
within a range of values
called bins. The height of
the bar equals the
number of times the data
point value fell within the
bin.
Example: the spread of the mean muon
lifetime based on an 31-hour measurement
of muon lifetime detections (in μs), the
height of bars corresponds to the
frequency of occurrence within a bin.
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Centre for Microcomputer Applications
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