Data Acquisition Overview

1

Using LabVIEW to acquire, analyze and record data

Data Collection

One shot

vs. time

Using the while loop

Using the DAQ for timing

2

DAQ set up for both

Choose RSE or differential, usually the latter

Choose voltage range to match your expected inputs

3

DAQ set up for while

Collect one sample

DAQ set up for DAQ timing

Collect N samples

Put controls on the front panel for rate and number of points

Timing

4

Saving Data

Use the Write to Measurement vi

For one shots or while loop control set up: Append to File

One File onlyOne header onlyOne time column only

General set up

For DAQ timing: Use next available file name.

5

Power Spectra

Use Spectral Analysis

Set to power spectrum, linear

Use DAQ timing

Number of points must be a power of 2, N = 2k

Sampling frequency (rate) must be high enough that half the frequency,the so-called Nyquist frequency,

exceeds the highest expected frequency

6

(Maximum sampling frequency for USB6009 is 48 kHz)

7

Zero Offset

Correct using a high pass filter

Install a control for the cut-off frequency

Aliasing

Test for by changing the sampling frequency

Other Power Spectra Issues

8

Power spectra amplitudes and frequencies

Use the Peak Detector vi

Create controls for threshold and peak/valley

Create indicators for number detected, locations and amplitudes(but see below)

Wire the output of the Spectral Analysis vi to the X (input) terminalof the Peak Detector

Optional: Multiply the output of the locations terminal by rate/(number of points)

to convert location to frequency

9

DAQ

Filter

Spectrum

Peaks

File

Raw data

The spectrum

I think we can record peaks as well,but I haven’t done it yet.

Spectral Analysis Schematic

10

Data Analysis Overview

What to do with your data when you’ve got itsitting in an Excel file

11

Possible tasks

Calibration, interpolation

Deducing constants in a theory

Deducing a theory

Characterizing variation in material properties

12

Calibration, interpolation

Generally a polynomial trendline is good enough

Assess the fit using R2, which you get for free, but which isn’t as good as

Standard deviation of the fit

€

s =

y i − y i( )2

i

∑n − k

(We have not explored techniques by which we can choose a “best” k.)

13

Characterization of Material Properties

You can use interpolation if you are fully ignorant

You can fit models if you have one

If you have time, energy and intuition, you can perhaps dream up a model

and assess it!

We looked at the Andrade model for the viscosity of water

14

Deducing Constants in a Theory

Write out the theory

Beat your data into a form that you can fit in Excel

Find the trendline

Convert back to theory

Assess the result using s.

15

Bernoulli Example

Theory:

€

h = h0 − CD

AE

AT

2gh0 t +1

2gCD

2 AE

AT

⎛

⎝ ⎜

⎞

⎠ ⎟

2

t 2

€

Plot h vs. t and fit a quadratic equation.

Calculate s for the fit

Is s consistent with the expected errors in the data?

Do the two values of CD you calculate agree with each other?

16

Cooling Curve Example

Theory:

€

T = Tf + Ti − Tf( )e−kt

You need to know, measure or estimate Tf.

Plot ln(T-Tf) vs. t

Fit a linear trendline: m = -k and b = ln(Ti-Tf)

Assess the fit in the original data:

€

s =

Ti − T i( )2

i

∑n − 2

€

T = exp b − mt( )

17

Deducing a Theory (Boyle’s Law)

Plot the data and look at it

18

Looks good, but what is it?

It’s not linear

You can make a polynomial fit, but . . .

there’s no physics in that — not a good idea

Note: p = 0 —> V —> ∞; V —> 0 —> p —> ∞.

A power law might be a good thing; plot ln(p) vs. ln(V).

19

20

Nice trendline (which you should assess)

The linear term is the exponent, looks like -1.

Carry on with the hypothesis pV = constant.

(We did this and I won’t do it again here.)