Transcript CE/ARE 397 Indoor Air Quality: Field Measurements

Objectives
• Regression analysis
• Sensor signal processing
Regression analysis
Single variable:
Minimum number of points depends on number of
variable in the function (3 for the function above).
Using the data we can set the system of equation to
find the coefficients.
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Lagrange interpolation
Rewrite:
Find coefficients:
General form:
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Regressing analysis for large pool
of data (function fitting)
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From last class
• Does correlation where R2=0.82 represent a
good data modeling?
Coefficient of determination
Total sum of squares:
Mean:
Sum of squares of residuals :
Anscombe's quartet
• Example of statistical misinterpretation of data
- all data have the same Mean (for x and y), Variance (for x and y)
- correlation R2: 0.816, linear regression: y=3.00+0.500·x
Anscombe's quartet
• Example of statistical misinterpretation of data
- all curves have the same Mean (x, y), Variance (x, y)
- correlation R2: 0.816, linear regression
Data set B
Data set A
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Data set C
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Data set D
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Moral of the story
Francis Anscombe (in 1973) demonstrated
• the importance of graphing data before
analyzing it
• the effect of outliers on statistical properties
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Model of complex system based on
experimental data
Example: chiller model
TOA
T Condensation
o
water TCWS=5 C
TCWR=11oC
Building users (cooling coil in AHU)
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Chiller model
P  PNOMINAL  CAPFT  EIRFPL
Impact of temperatures:
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CAPTF  a1  b1  TCW S  c1  TCW

d

T

e

T
S
1
OA
1
OA  f1  TCW S  TOA
Impact of capacity:
EIRFPLR  a3  b3  PLR  c3  PLR
PLR 
Q ( )
QNOMINAL
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Two variable function fitting
Example
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q[kW]
25 C
35 C
45 C
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Tevaporator [C]
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Fundamentals of Signal Processing
I
Sensor:
RTD, thermistor, hot wire, …..
V
R
V=I·R
Two approaches:
- Constant Voltage Source
- Constant Current Source
Cable Losses
DC signal [mV]
cable
Sensor
Voltage drop in the cable
Rcable=l·r (l length of cable , r resistance per unit of length)
r = f ( voltage, current, diameter, material )
Rcable can be same order of value like DC signal
- Use same length of cables (shorter if possible)
- Size diameter of cables to have significantly smaller voltage
drop in cable than DC signal
Signal
processing
Signal noise
AC current [120V]
cable
DC signal [mV]
Signal
processing
Sensor
Climate chamber
Current Induction
(signal nose)
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noise
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Magnetic field
supply
return
T [C]
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0
2
hour
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Signal noise filters
A low pass filter is placed on the signal wires between a signal and an A/D board. It stops frequencies greater
than the cut off frequency from entering the A/D board's analog or digital inputs.
The key term in a low pass filter circuit is CUT OFF FREQUENCY. The cut off frequency is the frequency above
which no variation of voltage with respect to time may enter the circuit. For example, if a low pass filter had a cut off
frequency of 30 Hz, the type of interference associated with line voltage (60Hz) would be filtered out but a signal of
25 Hz would be allowed to pass
A low pass filter may be constructed from on resistor R and
one capacitor C. The cut off frequency Fc is determined
according to the formula:
Fc= 1/2*Pi*C
R= 1/2*Pi*C*Fc
See the following diagram
Data Acquisition Device
Analog signal collection
Each Channel has:
- Current source
- ± connectors for Voltage measurement
I (variable A)
+
Measuring signal
to data acquisition
-
Current source
(constant V)
Analog signal collection
Voltage measurement ±
Voltage measurement
Current measurements
Wheatstone bridge
Wheatstone bridge
Wheatstone bridge
+
Known resistor
R2
Vo
+
R1
-
Vo
Calculate R4
Our sensor
Converting Analog signal to
Digital signal
Analog-to-digital converter (ADC)
- electronic device that converts analog signals to an equivalent digital form
- heart of most data acquisition systems
Loss of information in conversion,
but no loss in transport and processing