KD2 Pro 7 KD2 PRO THEORY
sought which minimize the difference between model and measured
values of temperature rise. Temperature of the needle is measured,
so ∆T is first computed by subtracting the initial temperature from
all readings. Temperature rise is further scaled by multiplying by 4π
and dividing by q. If we call this new temperature variable T
∗
, then
we find the values of k and D that minimize the sum of squares of
error.
SSE =
X
(T
∗
i
− M
∗
i
)
2
(10)
where the T
∗
i
are the measured values and the M
∗
i
are values modeled
with Equation 9. Equation 11 shows the standard error of estimate
for the measurements.
S
yx
=
r
SSE
n
(11)
where n is the number of measurements. The units of S
yx
are mC/W .
It can be made dimensionless if it is multiplied by the thermal con-
ductivity, k. This dimensionless value gives the error in fitting the
model to data as a value independent of heater current or the ther-
mal conductivity of the medium. The KD2 Pro computes err as in
equation 12.
err = kS
yx
(12)
It is a dimensionless measure of the goodness of fit of the model to
the data. It can be converted to temperature by dividing by k and
multiplying by q.
Note: The Err term is not a rigorous statistical indicator of mea-
surement quality, but it serves as a qualitative quality indicator.
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