DH Instruments COMPASS FOR MOLBOX, User Manual

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COMPASS

for molbox™ User’s Manual
© 1998-2003 DH Instruments, Inc .
Page 192
19.7 BEST FIT
All best fit values in COMPASS are determined using the least squares method. This defines a
selectable order polynomial equation that defines a line (or curve) that minimizes the sum of the squares
of the distances from the calculated line (or curve) to the actual line (or curve). A set of general equations
is described below. Based on the order of the polynomial fit, a system of equations is described. Solving
these equations for each of the polynomial coefficients determines the resultant polynomial equation.
b n b x b x b x y
o j
j
n
j m j
m
j
n
j
j
n
j
n
+ + + =
= = = =
∑ ∑ ∑ ∑
1 2
1
2
1 1 1
.....
b x b x b x b x x y
o j
j
n
j
j
n
j m j
m
j
n
j j
j
n
j
n
+ + + =
= =
+
= = =
∑ ∑ ∑ ∑ ∑
1
1
1
2
2
1
3 1
1 1 1
.....
•
•
b x b x b x b x x y
o j
m
j
n
j
m
j
n
j
m
m j
m m
j
n
j
m
j
j
n
j
n
+ + + =
=
+
=
+ +
= = =
∑ ∑ ∑ ∑ ∑
1
1
1
1
2
1
2
1 1 1
.....
VARIABLE DESCRIPTION
n
Number of X and Y points taken.
m
The order of the polynomial to fit. First order m = 1, second order
m = 2 and so on.
b
o ,
b
1 ..
Polynomial fit coefficients.
x
j
X axis data. This may be either the DUT or reference flow. It depends
on the purpose of the best fit. Typically, it is the DUT flow.
y
j
Y axis data. The data may be either the DUT or reference flow. It depends
on the purpose of the best fit. Typically, it is the reference flow.
19.8 LINEARITY
COMPASS determines the terminal based linearity of the DUT errors relative to the reference readings.
The linearity value is included in the <Calculations> section of the Data File (see Section 18.4).
There are two possible linearity calculations depending upon the test point sequence.
If the test point sequence is made up of corresponding ascending and descending (or vice-versa) points,
linearity is calculated by taking the average between corresponding DUT flows, drawing a straight line
between the minimum and maximum DUT flows and determining the maximum deviation of any average
DUT flow from this line. In this case, hysteresis is also calculated (see Section 19.9).
If the test point sequence is not made up of corresponding ascending and descending (or vice-versa)
points, linearity is calculated by drawing a straight line between the minimum and maximum DUT flows
and determining the maximum deviation of any DUT flow from this line. In this case, hysteresis is not
calculated (see Section 19.9).