The earlier chapters in this book have been essentially concerned with describing ways of producing high-quality, error-free data at the output of a measurement system. Having got the data, the next consideration is how to present it in a form where it can be readily used and analysed. This chapter therefore starts by covering the techniques available to either display measurement data for current use or record it for future use. Following this, standards of good practice for presenting data in either graphical or tabular form are covered, using either paper or a computer monitor screen as the display medium. This leads on to a discussion of mathematical regression techniques for fitting the best lines through data points on a graph. Confidence tests to assess the correctness of the line fitted are also described. Finally, correlation tests are described that determine the degree of association between two sets of data when they are both subject to random fluctuations.
11.1 Display of measurement signals
Measurement signals in the form of a
varying electrical voltage can be displayed either by an oscilloscope or else
by any of the electrical meters described earlier in Chapter 6. However, if
signals are converted to digital form, other display options apart from meters
become possible, such as electronic output displays or using a computer
monitor.
11.1.1 Electronic output displays
Electronic displays enable a
parameter value to be read immediately, thus allowing for any necessary
response to be made immediately. The main requirement for displays is that they
should be clear and unambiguous. Two common types of character format used in
displays, seven-segment and 7 ð 5 dot matrix, are shown in Figure 11.1. Both
types of display have the advantage of being able to display alphabetic as well
as numeric information, although the seven-segment format can only display a
limited nine-letter subset of the full 26-letter alphabet. This allows added
meaning to be given to the number displayed by including a word or letter code.
It also allows a single
display unit to send information
about several parameter values, cycling through each in turn and including
alphabetic information to indicate the nature of the variable currently
displayed.
Electronic output units usually
consist of a number of side-by-side cells, where each cell displays one
character. Generally, these accept either serial or parallel digital input
signals, and the input format can be either binary-coded decimal (BCD) or
ASCII. Technologies used for the individual elements in the display are either
light-emitting diodes (LEDs) or liquid-crystal elements.
11.1.2 Computer monitor displays
Now that computers are part of the
furniture in most homes, the ability of computers to display information is
widely understood and appreciated. Computers are now both cheap and highly
reliable, and they provide an excellent mechanism for both displaying and
storing information. As well as alphanumeric displays of industrial plant
variable and status data, for which the plant operator can vary the size of
font used to display the information at will, it is also relatively easy to
display other information such as plant layout diagrams, process flow layouts
etc. This allows not only the value of parameters that go outside control
limits to be displayed, but also their location on a schematic map of the
plant. Graphical displays of the behaviour of a measured variable are also
possible. However, this poses a difficulty when there is a requirement to
display the variable’s behaviour over a long period of time since the length of
the time axis is constrained by the size of the monitor’s screen. To overcome
this, the display resolution has to decrease as the time period of the display
increases.
Touch screens are the very latest
development in computer displays. Apart from having the ability to display the
same sort of information as a conventional computer monitor, they also provide
a command-input facility in which the operator simply has to touch the screen
at points where images of keys or boxes are displayed. A full ‘qwerty’ keyboard
is often provided as part of the display. The sensing elements behind the
screen are protected by the glass and continue to function even if the glass
gets scratched. Touch screens are usually totally sealed, and thus provide
intrinsically safe operation in hazardous environments.
11.2 Recording of measurement data
Many techniques now exist for
recording measurement data in a form that permits subsequent analysis,
particularly for looking at the historical behaviour of measured parameters in
fault diagnosis procedures. The earliest recording instruments used were
various forms of mechanical chart recorder. Whilst many of these remain in use,
most modern forms of chart recorder exist in hybrid forms in which
microprocessors are incorporated to improve performance. The sections below
discuss these, along with other methods of recording signals including digital
recorders, magnetic tape recorders, digital (storage) oscilloscopes and
hard-copy devices such as dot-matrix, inkjet and laser printers.
11.2.1 Mechanical chart recorders
Mechanical chart recorders are a
long-established means of making permanent records of electrical signals in a
simple, cheap and reliable way, even though they have poor dynamic
characteristics which means that they are unable to record signals at
frequencies greater than about 30 Hz. They have particular advantages in
providing a non-corruptible record that has the merit of instant ‘viewability’,
thereby satisfying regulations in many industries that require variables to be
monitored and recorded continuously with hard-copy output. ISO 9000 quality
assurance procedures and ISO 14000 environmental protection systems set similar
requirements, and special regulations in the defence industry go even further
by requiring hard-copy output to be kept for ten years. Hence, whilst many
people have been predicting the demise of chart recorders, the reality of the
situation is that they are likely to be needed in many industries for many
years to come. This comment applies particularly to the more modern, hybrid
form of chart recorder, which contains a microprocessor to improve performance.
Mechanical chart recorders are either of the galvanometric type or potentiometric
type. Both of these work on the same principle of driving chart paper at a
constant speed past a pen whose deflection is a function of the magnitude of
the measured signal. This produces a time history of the measured signal.
Galvanometric recorders
These work on the same principle as a
moving-coil meter except that the pointer draws an ink trace on paper, as
illustrated in Figure 11.2, instead of merely moving against a scale. The
measured signal is applied to the coil, and the angular deflection of this and
its attached pointer is proportional to the magnitude of the signal applied.
Inspection of Figure 11.3(a) shows that the displacement y of the pen across
the chart recorder is given by y = R sin θ. This sine relationship between the
input signal and the displacement y is non-linear, and results in an error of
0.7% for deflections of ±10°. A more serious problem arising from the pen
moving in an arc is that it is difficult to relate the magnitude of deflection
with the time axis. One way of overcoming this is to print a grid on the chart
paper in the form of circular arcs, as illustrated in Figure 11.3(b).
Unfortunately, measurement errors often occur in reading this type of chart, as
interpolation for points drawn between the curved grid lines is difficult. An
alternative solution is to use heat-sensitive chart paper directed over a
knife-edge, and
to replace the pen by a heated
stylus, as illustrated in Figure 11.4. The input–output relationship is still
non-linear, with the deflection y being proportional to tan θ as shown in
Figure 11.5(a), and the reading error for excursions of ±10° is still 0.7%.
However, the rectilinearly scaled chart paper now required, as shown in Figure
11.5(b), allows much easier interpolation between grid lines
Neglecting friction, the torque
equation for a galvanometric recorder in steady state can be expressed as:
Torque due to current in coil =
Torque due to spring
Following a step input, we can write:
Torque due to current in coil D
Torque due to spring C Accelerating torque or:
KiI
= Ksθ + Jθ (11.1)
where I is the coil current, θ is the
angular displacement, J is the moment of inertia and Ki and Ks
are constants. Consider now what happens if a recorder with resistance Rr
is connected to a transducer with resistance Rt and output voltage Vt,
as shown in
Figure 11.6. The current flowing in
steady state is given by: I = Vt/(Rt + Rr).
When the transducer voltage Vt is first applied to the recorder
coil, the coil will accelerate and, because the coil is moving in a magnetic
field, a backward voltage will be induced in it given by
which is an expression describing the
measurement sensitivity of the system.
The dynamic characteristics of a
galvanometric chart recorder can therefore be represented by one of the
output-reading/time characteristics shown in Figure 2.12. Which particular
characteristic applies depends on the damping factor of the instrument. At the
design stage, the usual aim is to give the instrument a damping factor of about
0.7. Achieving this is not straightforward, since the damping factor depends
not only on the coil and spring constants (Ki and Ks) but
also on the total circuit resistance (Rt + Rr) . Adding a
series or parallel resistance between the transducer and recorder,
as illustrated in Figure 11.7,
respectively reduces or increases the damping factor. However, consideration of
the sensitivity expression of (11.3) shows that any reduction in the damping
factor takes place at the expense of a reduction in measurement sensitivity.
Other methods to alter the damping factor are therefore usually necessary, and
these techniques include decreasing the spring constant and system moment of
inertia. The second order nature of the instrument’s characteristics also means
that the maximum frequency of signal that it can record is about 30 Hz. If
there is a need to record signals at higher frequencies than this, other
instruments such as ultra-violet recorders have to be used.
Galvanometric recorders have a
typical quoted measurement inaccuracy of ±2% and a resolution of 1%. However,
their accuracy is liable to decrease over time as dirt affects performance, particularly
because it increases friction in the bearings carrying the suspended coil. In
consequence, potentiometric types of recorder are usually preferred in modern
instrumentation systems.
Potentiometric recorders
Potentiometric recorders have much better
specifications than galvanometric recorders, with a typical inaccuracy of ±0.1% of full scale and measurement resolution
of 0.2% f.s. being achievable. Such instruments employ a servo system, as shown
in Figure 11.8, in which the pen is driven by a servomotor, and a potentiometer
on the pen feeds back a signal proportional to pen position. This position
signal is compared with the measured signal, and the difference is applied as
an error signal that drives the motor. However, a consequence of this electromechanical
balancing mechanism is to give the instrument a slow response time in the range
0.2–2.0 seconds. This means that potentiometric recorders are only suitable for
measuring d.c. and slowly time-varying signals. In addition, this type of recorder
is susceptible to commutator problems when a standard d.c. motor is used in the
servo system. However, the use of brushless servo motors in many recent models
overcomes this problem. Newer models also often use a non-contacting ultrasonic
sensor to provide feedback on pen position in place of a potentiometer. Another
recent trend is to include a microprocessor controller (this is discussed under
hybrid chart recorders).
Circular chart recorders
Before leaving the subject of
standard mechanical chart recorders, mention must also be made of circular
chart recorders. These consist of a rotating circular paper chart, as shown in
Figure 11.9, which typically turns through one full revolution in 24 hours,
allowing charts to be removed once per day and stored. The pen in such
instruments is often driven pneumatically to record 200–1000 mbar (3–15 psi)
pneumatic process signals, although versions with electrically driven pens also
exist. This type of chart recorder was one of the earliest recording instruments
to be used and, whilst they have now largely been superseded by other types of
recorder, new ones continue to be bought for some applications. Apart from
single channel versions, models recording up to six channels, with traces in
six different colours, can be obtained.
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