Campbell Scientific CR10X Measurement and Control System User Manual

Page 171

SECTION 10. PROCESSING INSTRUCTIONS

10-13

The Averaging Period Processing occurs
whenever the number of input samples entered
in Parameter 7 is satisfied or whenever an
Output Interval occurs (i.e., whenever the
Output Flag is set). Results from these
calculations are stored sequentially in Input
Storage locations starting with the location
specified in Parameter 9. The calculations
performed are shown below, where N is the
number of input samples in the averaging
period:

Means:

M(X) =

ΣX/N

Variances:

V(X) =

ΣX

/N - (

ΣX/N)

Standard Deviations:

SD(X) = V(X)

1/2

Covariances:

CV(X,Y) =

ΣXY/N -

ΣX ΣY/N

Correlations:

CR(X) = CV(X,Y)/(SD(X)SD(Y))

NOTE:

1. The square root algorithm in the
CR10X returns a result of 0 for
negative arguments.

2. The divide algorithm returns the
largest floating point number possible
(

displayed as

99999) for a

divide by 0.

3. When computing the variance of a
constant signal, round off error
produces a small negative result.
The CR10X returns a 0 for the
square root of a negative number;
therefore, the standard deviation is
set to 0. If the signal is also used in a
correlation calculation, division by 0
returns an overrange value for the
correlation result.

If a fast execution interval is specified, it is
possible that the combined execution times of
the input and averaging period processing may
exceed the program table execution interval.
The occurrence of an execution interval Overrun
(see Section 1.1.1 of CR10X Operator's Manual)
is noted by decimal points on either side of the G
in LOG (

∗0 MODE). This results in the omission

of one input sample. The calculations are not
affected, however, since the number of input
samples is incremented only when valid input

processing occurs. Averaging period processing
occurs only when the number of input samples
specified in Parameter 7 is accumulated.

Regardless of whether all of the input samples
for the averaging period (specified in Parameter
7) have occurred or not, averaging period
processing occurs whenever the Output Flag is
set. This accommodates situations where the
Output Interval may not be an integer multiple of
the averaging period. If for example a 30 minute
Output Interval is set by Instruction 92 and an 8
minute averaging period is specified by
Parameter 7, then three 8 minute and one 6
minute calculations will occur. The proper
weighting of these values in producing the final
output is described below.

The Output Processing occurs only at the
Output Interval and involves averaging the
statistical results obtained at the averaging
periods. These final results are then stored
sequentially in Input Storage beginning with the
location specified in Parameter 9. The Sample
Instruction 70 must be used to transfer the data
to Final Storage. All but the last averaging
period in the Output Interval will contain the
same number of input scans as specified by
Parameter 7. To insure that results from the
averaging periods contribute to the final result
proportional to their averaging periods, the
output processing uses the following equation:

RF = (NR1 + NR2 + .... + N'RL)/NT

RF is the final result
R1 R2, etc., are the results from the averaging

period processing

RL is the result from the last averaging period

in the Output Interval

is the number of input samples in the
specified averaging period (Parameter 7)

N' is the number of input scans in the last

averaging period

NT is the total number of input samples

processed in the Output Interval

INTERMEDIATE STORAGE REQUIREMENTS

The number of Intermediate locations will
depend upon the number of input values and
outputs desired:

Define K as the number of input values.

Define S as the maximum of either the
variances, standard deviations, or C, where