AE547 2 Introduction
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Transcript of AE547 2 Introduction
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Manometers
Pitot tubes
Thermocouples o w re sys ems
a. Anemometers
b. Probes
- Simple- Slented
- Cross-wire
LDA (Laser Doppler Anemometry)
PIV (Particle Image Velocimetry)
----------------------------------------------
Data Acquisition System
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Typical PC-Based DAQ System
Transducers
Signal conditioning
DAQ hardwareSoftwarehttp://zone.ni.com/
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Data Acquisition (DAQ) Fundamentals
Data acquisition involves gathering signals from measurement sources
and digitizing the signal for storage, analysis, and presentation on a PC.
Data acquisition (DAQ) systems come in many different PC technology formsor grea ex y w en c oos ng your sys em.
Scientists and engineers can choose from PCI (Peripheral Component
, , , , , ,
Ethernet data acquisition for test, measurement, and automation applications.
system :
Transducers and sensors
Signal conditioning
DAQ hardware
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http://zone.ni.com/devzone/cda/tut/p/id/4811
PXI is the open, PC-based platform for test, measurement, and control
PXI systems are composed of three basic components chassis, systemcontroller, and peripheral modules
Standard 8-Slot PXI Chassis
Embedded System Controller andSeven Peripheral Modules
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A t ical DAQ s stem with National Instruments SCXI si nal conditionin
accessories
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Transducers and sensors
rans ucer s a ev ce a conver s a p ys ca p enomenon n o ameasurable electrical signal, such as voltage or current.
the transducers to convert the physical phenomena into signals measurable
by the DAQ hardware.
Phenomenon Transducer
Temperature Thermocouple, RTD, Thermistor Light Photo Sensor
Sound Microphone
Force and Pressure Strain Gage
Piezoelectric Transducer
Position and Displacement Potentiometer, LVDT, Optical Encodercce era on cce erome er
pH pH Electrode
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Signals
The a ro riate transducers convert h sical henomena into measurable
signals.
However different si nals need to be measured in different wa s. For this
reason, it is important to understand the different types of signals and their
corresponding attributes.
Signals can be categorized into two groups:
Analog
Digital
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Analog Signals
.
signals include voltage, temperature, pressure, sound, and load. The three primary
characteristics of an analog signal include level, shape, and frequency
Because analog signals can take on any value, level gives vital
information about the measured analog signal. The intensity of a
light source, the temperature in a room, and the pressure insidea c am er are a examp es a emons ra e e mpor ance o
the level of a signal.
Primary Characteristics of an Analog Signal
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Digital Signals
A digital signal cannot take on any value with respect to time.Instead, a digital signal has two possible levels: high and low.
Digital signals generally conform to certain specifications that define characteristics
of the signal. Digital signals are commonly referred to as transistor-to-transistor logic
(TTL). TTL specifications indicate a digital signal to be low when the level falls within
0 to 0.8 V, and the signal is high between 2 to 5 V.
The useful informationthat can be measured
includes the state (on or
off, high or low ) and the
rate of a di ital how thedigital signal changes
state with respect to time
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Signal Conditioning
Sometimes transducers generate signals too difficult or too dangerous tomeasure directly with a DAQ device.
For instance, when dealing with high voltages, noisy environments, extreme high
and low signals, or simultaneous signal measurement, signal conditioning is
essential for an effective DAQ system. Signal conditioning maximizes the
accuracy of a system, allows sensors to operate properly, and guarantees safety.
Signal conditioning accessories can be used in
a variety of applications including:
AttenuationIsolation (The system being monitored may
-
damage the computer without signal
conditioning)
Simultaneous sampling
Sensor excitation
Multi lexin A common techni ue for
measuring several signals with a singlemeasuring device is multiplexing.)
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Signal
conditioning
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DAQ Hardware
.
It primarily functions as a device that digitizes incoming analog signals so that the
computer can interpret them. Other data acquisition functionality includes:
Analog Input/Output
Digital Input/Output
Counter/Timers Multifunction - a combination of analog, digital, and counter operations on a single
device
NI Wi-Fi Data Acquisition
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CPU
Central Processing
101011
Unit
Address ControlData
A/D
ConverterSampled Analog
Input Signal Digital Output
Input
Device
Keyboard
Disk
A/D Converter
111
Buss
110
101Digital
OutputMemory
010
011
Output
Device
CRT
Printer
Disk
000
001
0 Full
Scale1/2 LSB
Computer monitors
na og npu
LSB: least significant bitRef: http://cobweb.ecn.purdue.edu/~aae520/
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Full scale volta e=23range R=8V
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Dynamic Response of
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A static measurement of a physical quantity is
time.
The deflection of a beam under a constant load
deflection would vary with time (dynamic
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- - -,
A system may be described in terms of a general
var a e x t wr tten n erent a equat on orm as:
where F(t) is some forcing function imposed on the system.
.
A zeroth-order system would be governed by:
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A first-order system is governed by:
A second-order system is governed by:
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The zeroth order system indicates that the system variable x(t) will
follow the input forcing function F(t) instantly by some constant
value:
e cons an a0 s ca e e s a c sens v y o e sys em.
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The first order system may be expressed as:
The = a1/a0 has the dimension of timean s usua y ca e e me cons an
of the system.
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For step input : F(t)=0 at t=0F(t)=A for t>0
Along with the initial condition x=x at t=0
The solution to the first order system is:
where
Steadystate
Transientresponse of
(call x)
The same solution can be written in dimensionless forms as:
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Dynamic Response of Measurement
Systems
ero r er ys em:
Input signalOutput signal
)()( tFKtx =
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npu s gna examp es:
- 0
Unit step function
(Heaviside function)Shifted unit step function
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Dynamic Response of Measurement
dx=
Systems
Step response
-
dt
Impulse response
)1()0( /teFKx =
/)0( teFKx =11
5.=
ude
0.6
0.70.8
.
0.6
0.7
0.8
0.9
litude
1=2=
Amplit
0.3
0.4
0.5
2=0.3
0.4
0.5Am
0 2 4 6 8 100
0.1
.
/t
1=
5.=
/t0 2 4 6 8 10
0
0.1
.
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Dynamic Response of Measurement
First Order S stemInput OutputSystems
Sinusoidal Response )sin(1 22
++
= tx
s n=
-
tan =
Amplitude Decrease and Phase Shift
0.6
0.8
1
-20
-10
0
GaindB
Input
-0.2
0
0.2
.
amplitude
10-1
100
101-30
0
deg
Output
-0.8
-0.6
-0.4
-1 0 1
-
-60
-90
Phase
0 0.5 1 1.5 2 2.5-1
time
Bode Plot
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Dynamic Response of Measurement
Systems
Step response - Second Order System
1.8
2
22
2
dxxd =
1.2
1.4
.
ude
-
frequencynatural-
2
n
nnndtdt
0.6
0.8
1
Am
plit
res onsefastestfor-7.
nsoscillationo-dampingcritical-1
=
=
0.2
0.4
dam ed criticallfortimethehalfin
valuestaticof5%tocomesSystem
overshoot5%
0 5 10 15 20tn
systems
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Dynamic Response of Measurement
Second Order S stem - Sinusoidal Res onseSystems
=+
==
2
1
22
2
1
2
tan)sin()0(
x)sin()0( ntFK
tFF
n
nn
(dB)
ase
(deg)
n/
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Dynamic Response of Measurement
Systems
econ r er ys em - mpu se esponse
)1sin()0( 2 += teFKx
n
tn
0.8
1Impulse response - Second Order System
0.4
0.6
e
-0.2
0
0.2
Amplitu
-0.6
-0.4
0 20 40 60 80 100-0.8
time
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1
1 .2
1
1 .2
0 .2
0 .4
0 .6
.
AmplitudeRatio
0 .2
0 .4
0 .6
.
AmplitudeRatio
0 1 0 2 0 3 0 4 0 5 00
F r equenc y ( H z )
0 1 0 2 0 30
F r equenc y ( H
Low Pass Filter High Pass Filter
Removes High Frequency Noise
(Such as 60, 120 Hz)
0 .8
1
1 .2
eR
atio 0 .8
1
1 .2
eR
atio
0
0 .2
0 .4
.
Amplitud
0
0 .2
0 .4
.
Amplitud
F re q ue nc y (H z) F re q ue nc y (H z)
Band Pass Band Stop
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Example: MUSIC
Basically, the equalizer in your stereo is nothing more than a set of band
pass filters in parallel. Each filter has a different frequency band that it
con ro s. e equa zer s use o a ance e s gna over eren
frequencies to shape the noise (music)
amplitude
Dr. Peter Avitabile University of Massachusetts Lowell
frequency
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The instrument that is used to make measurements will have some verydefinite frequency characteristics. This defines the usable frequency range
of the instrument. As art of the lab and measurements taken there was a
different usable frequency range for the oscilloscope and the digital
multimeter
amp u e amp u e
Dr. Peter Avitabile University of Massachusetts Lowell
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amplitude amplitude
Dr. Peter Avitabile University of Massachusetts Lowell
frequency requency
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In addition to instruments, the actual transducers used to makemeasurements also have useful frequency ranges. For instance, a strain
gage accelerometer and a peizoelectric accelerometer have different useful
frequency ranges
amp u e amp u e
Dr. Peter Avitabile University of Massachusetts Lowell
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Fs = 100;t = 0:1/Fs:1;
* * * * * * *
. .
% DC plus 5 Hz signal and 40 Hz signal sampled at 100 Hz for 1 sec
2
1.5Total Signal
DC Level
0.5
plitude(volts)
Signal
-0.5
0A g requency
0 0.2 0.4 0.6 0.8 1-1
Time (sec)
http://cobweb.ecn.purdue.edu/~aae520/
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1 .5
2
Original1
1.2
- 1
- 0 . 5
0
0 .5
1
Amplitud
e(volts) Signal
Filter
Filtfilt0.2
0.4
0.6
0.8
AmplitudeRatio
Low Passecovers
DC + 3Hz
. . .T i m e ( s e c )
0 .5
1
1 .5
2
de(vo
lts)
0 10 20 30 40 50Frequency (Hz)
0.8
1
1.2
eRatio
Cheby2
High Pass Recovers
0 0 . 2 0 . 4 0 . 6- 1
- 0 . 5
0
T i m e ( s e c )
Amplit
2
0 10 20 30 40 500
0.2
0.4
.
Frequency (Hz)
Amplitud
1 2
- 0 . 5
0
0 .5
1
1 .5
Amplitude(volts)
0.4
0.6
0.8
1
.
AmplitudeRatio Cheby2Band Pass Recovers
3Hz
0 0 . 2 0 . 4 0 . 6- 1 . 5
- 1
T i m e ( s e c )
1 .5
2
0 10 20 30 40 500
0.2
Frequency (Hz)
1
1.2
- 1
- 0 . 5
0
0 .5
1
Amplitude(volts)
0.2
0.4
0.6
0.8
AmplitudeRatio
Cheby2
Stop Band
ecovers
DC + 40Hz
. . .T i m e ( s e c )0 10 20 30 40 50
Frequency (Hz)
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easuremen rror
True Value
as rror
Systematic Error
Remains Constant During Test
i
Bias Error
Calibration
or judgement
Random ErrorPrecision ( Random Error )Precision Index - Estimate ofxxii =
Total Error
Deviation
A statistic, s, is calculated
from data to estimate the recisionerror and is called the precision
index
N
i = + i
11
= N
xx
s
i
We may categorize bias into five classes :
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o large known biases,
o small known biases,
o large unknown biases and
o small unknown biases that may have unknown sign () or known sign.
The large known biases are eliminated by comparing the instrument to a standard
instrument and obtaining a correction. This process is called calibration.
Small known biases may or may not be corrected depending on the difficulty of the
correction and the magnitude of the bias.
The unknown biases, are not correctable. That is, we know that they may exist but we do
not know the sign or magnitude of the bias.
Five types of bias errors
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.
The introduction of such errors converts the controlled measurement process
into an uncontrolled worthless effort.
Large unknown biases usually come from human errors in data processing,
incorrect handling and installation of instrumentation, and unexpectedenvironmental disturbances such as shock and bad flow profi les. We
must assume that in a well controlled measurement process there are no
large unknown biases. To ensure that a controlled measurement process
exists, all measurements should he monitored with statistical quality control
charts.
Measurement Error
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Precise, Accurate (Unbiased) Precise, Inaccurate (Biased)
Im recise Accurate Unbiased Im recise Inaccurate Biased
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Instrument
Readin s
Truea ue
&precise
butprecise
butaccurate
&imprecise
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arame er s ma on
A desirable criterion in a statistical estimator is unbiasedness. A statistic is
unbiased if the expected value of the statistic is equal to the parameter being
estimated.
Unbiased estimators of the parameters, , the mean, and , the standarddeviation are:
xN
i Estimation of meanN
x=
[ mean(data) ]
)(1
2
=
xxN
i Estimation of standard deviation,
1N
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Estimate of the Probability Density Function
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Estimate of the Probability Density Function
[ hist(data,# of bins) ]
700
800
500
600
200
300
850 900 950 1000 1050 11000
100
(data measured)
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Examine the data for consistent. No matter how hard one tries, there will always be some datapoints that appear to be grossly in error. The data should follow common sense consistency, and
points that do not appear "proper" should be eliminated. If very many data points fall in the
category of "inconsistent" perhaps the entire experimental procedure should be investigated for
gross mistakes or miscalculations.
Perform a statistical analysis of data where appropriate. A statistical analysis is only appropriatewhen measurements are repeated several times. If this is the case, make estimates of such
parameters as standard deviation, etc.
Estimate the uncertainties in the results. These calculations must have been performed in
advance so that the investigator will already know the influence of different variables by the time
the final results are obtained.
Anticipate the results from theory. Before trying to obtain correlations of the experimental data,
the investigator should carefully review the theory appropriate to the subject and try to think some
information that will indicate the trends the results may take. Important dimensionless groups,
pertinent functional relations, and other information may lead to a fruitful interpretation of the data.
Correlate the data. The experimental investigator should make sense of the data in terms of
physical theories or on the basis of previous experimental work in the field. Certainly, the results
of the experiments should be analyzed to show how they conform to or differ from previous
investigations or standards that may be employed for such measurements.
(Ref. Holman, J. P., Experimental Methods for Engineers")