BSA Flow Software Installation and User's Guide - CSI

Software implementation
Updating mean value estimates:
t ←
Updating Variance and RMS estimates:
If calculations are based on old data, where all samples are available from
the beginning and no further samples will be acquired, the formulas above
are used directly.
During data acquisition temporary results are calculated and updated as new
samples arrive. A different approach is used to make fast and efficient
calculations in this case.
Store the total number of samples N as well as the sums ∑ i and t ∑ i i U
t .
(If you’re not using transit time weighting, ti=1 for all i and the former of the
summations will equal N).
Whenever a block of M new samples arrive, update these values:…
N ← N + M
∑
∑
∑
tU
←
( ∑t
) + ( )
N ∑t
M
( ∑tU
) + ( tU
) N ∑ M
… and recalculate the mean value according to formula (7-34).
(11)
(12)
(13)
Statistics can in principle be updated for each and every new sample arriving
in which case M=1.
Store and update the sample count and sums as above, plus the weighted sum
of squared velocity sample values:
2
2
( ∑ t U ) + ( t U ) N
M
2
t U ← ∑
-now an updated variance estimate can be calculated according to the
following:
=
∑
t ⋅
2
u 2
2
2
∑ tU
− ( ∑ tU)
N
⋅
( ∑ t)
N −1
(14)
-where the bias correction term at the end is used when no weigthing is
applied, and ignored when Transit Time weigthing is applieded.
Taking the square root of the updated variance estimate as in (7-36) will
produce an updated estimate of the RMS.
(15)
Combining the total number of samples now included with the updated
estimates of mean and variance from above, you will also be able to update
the confidence limit value for the estimated mean using formula (7-37) and
(7-41).
If the measured velocity is assumed normal distributed, the confidence limit
for the estimated variance and RMS can also be updated using formulas
(7-38), (7-39) & (7-41).
BSA Flow Software:Reference guide 7-103