regression/mean square error: larger values
mean a better fit) and r^2 (maximum = 1.0,
values within the range 0.97–1.0 are
acceptable) give a measure of the overall
fit. In addition, one should examine the
standard error (SE), 95% confidence limits
and t values of the parameters (para-
meter value/standard error). Multiple-pool
models usually give a higher F statistic and
r^2 than a single-pool model because there is
more ‘wiggle room’. However, this extra
flexibility is sometimes purchased at the
expense of less well-defined parameter
values (lower t).
The tvalue reflects the importance of a
given parameter in determining the overall
function value. If tis low, then the function
is insensitive to changes in that parameter
value. In Equation 10.5, for example, the
lag term L is less important than the
specific rate or asymptotic volume in deter-
mining Vt. The tvalue for L will always be
less than that for S. If we wish to use curve
fit parameters for comparative purposes,
rather than simply to summarize a data set,
then the preference is to produce a good fit
with the smallest possible number of well-
defined parameters.
Simple inspection of the appearance of
the calculated curve compared with the
data points provides a useful, though not
a sufficient, criterion for a good fit. It is
important to supplement numerical
analysis with common sense!
Some thought should be given to the
choice of data points used for curve fitting.
If the data approach an asymptote, then
points much beyond the asymptotic value
should be excluded from the fit. There is
otherwise a danger that ‘the tail may
wag the dog’ and that these constant or
very slowly changing data may unduly
influence the program’s choice of best
parameters to fit regions of the curve where
the data are changing rapidly.Pressure sensors, types and constructionWe live in a pressurized world and
pressure measurements must therefore
always involve pressure differences.
Pressure sensors vary in the standard
against which an unknown pressure is
measured. ‘Absolute’ sensors use a sealed
vacuum reference; ‘differential’ sensors use
a second pressure source; ‘gauge’ sensors
use atmospheric pressure as the reference.
The most common sensors are of the differ-
ential type. These become gauge sensors if
the reference port is left open to the atmos-
phere.
The sensing element of a solid-state
pressure sensor consists of four nearly
identical piezo-resistors (resistors whose
value changes with strain) buried within
the surface of a thin silicon diaphragm. A
pressure applied to this diaphragm causes
it to flex and to change its resistance. If a
voltage is applied across the resistor net-
work, resistance changes are transformed
into voltage changes. These changes can
then be amplified and used to measure
pressure.
Sensors are calibrated by attaching
them to a sealed bottle of known volume
containing medium and measuring the
changes in voltage output as known
volumes of CO 2 are injected into the bottle.
This calibration result will depend both on
the bottle size and on the atmospheric
pressure at the time of calibration. In this
way, the sensor output (Volts) can be
translated simply and directly into a gas
volume (Schofield and Pell, 1995b).232 P. Schofield