Journal of Accident Investigation

JOSEPH GREGOR
When the correlated data for this case were plotted as in
figure 9, the resulting curve fit turned out to be linear, but with
b = 0.9831. This indicated that the time-base in one unit
was operating at a constant but different rate when compared
with the other. If the CVR had been a tape-based unit, the
assumption would have been that the tape speed was off, and
the resulting transform applied to adjust the CVR data to match
the FDR data. However, since both units were solid-state in
this case, a different assumption was required.
Researching these correlation problems with the manufacturer
turned up an anomaly in the FDR recording system. In a typical
installation, data are fed to the FDR in groups identified by SRN.
Each group represents a repeating set of data points for the
various parameters being measured. These groups are sent to
the FDR at a rate of 1 per second – and each SRN is assumed to
represent 1 second of flight data. In this particular installation,
however, the data stream was being fed to the FDR at a rate
of 61 groups per minute. As a result, each SRN represented
roughly 60/61 = 0.9836 seconds of data, consistent with
transform results found for b. Once this transform was applied,
the corrected FDR on-key/off-key data were found to overlay
clearly with the CVR data at the offset originally determined by
the cross-correlation function.
CONSIDERATIONS FOR MORE COMPLEX
TRANSFORMS
Valid correlations may always be obtained by assuming
a linear transform as given in Eq. (2), provided that the
time-bases in both units are operating at a fixed, constant rate.
This will not be the case, however, if the time-base in one or
both units changes rate during the recording. This may occur in
the case of a solid-state recorder if power is momentarily lost to
one of the boxes. In this instance, a linear fit as in Eq. (2) would
still be valid on each side of the discontinuity. This may also
occur for a tape-based CVR due to power supply fluctuations
or mechanical changes in the tape drive mechanism. Either
of these factors could change the tape speed, and hence the
amount of information corresponding to 1 second of digitized
data. When played back at a constant speed, the effect will be
an apparent change in the time-base for that audio recording.
Note that, since a tape-based CVR is an analog device, there
is no reason to assume that the tape speed must change from
one discrete constant value to another discrete constant value.
Instead, the tape speed – and hence the time-base for the
playback – may in principle take on any analog value. A linear
transform as in Eq. (2) will not suffice in this case.
In the past, such correlations have been performed by
employing a piecewise linear fit to subsets of the recorded
data. These sections are then reassembled to obtain a single
contiguous data set. This is essentially equivalent to employing
Eq. (2) over segments of the data, and performing a curve fit to
obtain the values for b and C corresponding to a unique solution
within each segment. Matching solutions at each end, one
could obtain a transform for the entire data set of the form,
tcvr= b1 * tfdr + C1 t0 < tfdr ≤ t1
tcvr= b2 * tfdr + C2 t1 < tfdr ≤ t2
tcvr= b3 * tfdr + C3 t2 < tfdr ≤ t3
tcvr= b4 * tfdr + C4 t3 < tfdr ≤ t4
Eq. (5)
This method is not without its disadvantages. Picking the
limits required to obtain a correlation using a minimum number
of segments for the desired accuracy involves a significant
amount of labor. If the flow of time in one of the units varies
continuously, as may be expected for an analog device, the
number of segments required to obtain a good fit could become
extremely large. In addition, while the magnitude of the data
may match at the boundaries, the derivative of the resulting
curve will necessarily be discontinuous at the ends of each
segment – an unphysical result.
We may, however, extend this method to obtain a more
accurate result with far less labor by recalling from basic
calculus that any continuous function can be represented by
a number of straight line segments. The larger the number of
segments, the closer the resulting representation will come to
the true curve. The original curve can be reproduced exactly
in the limit that an infinite number of segments are employed.
This is nothing more than the description of a generalized curve
fit. An accurate correlation to any data set not yielding to a
linear fit may then be obtained by cross-correlating the data
to obtain a first-order time alignment, and then calculating a
cubic spline fit or similar generalized curve fit. This procedure
may be easily implemented on any desktop computer using a
wide variety of software tools. The results may be plotted as in
figure 9 to check the validity of the final solution.
CONCLUSIONS
A new method has been described for performing the
correlation of time as represented in the CVR with time
as represented in the FDR. This method employs the use
2 NTSB JOURNAL OF ACCIDENT INVESTIGATION, SPRING 2006; VOLUME 2, ISSUE 1