Step 2 – Optimization

Step 2 presented solutions with quantitative, non- probabilistic measure of slack within feasibility constraints。 All the infeasible solutions from Table 2 can be explained by Figure 7。 When CVR perturbations create a scenario where the CVR timeline recorded a radio transmission yet the FDR did not sample a microphone keying, an infeasible situation occurs; this is shown by CVRs in Figure 7。 One of the ways the scenario in Figure 7 can occur was shown in Case 9 of Table 2: a timebase of other than 1 in the CVR recording/playback。 This can occur in tape or solid-state units and is in fact part of the regulatory timebase tolerance limit of 。125% per hour。 The scope of this research effort limited the defined problem to a timebase of 1; however, the next section discusses model modifications。

It is intuitively expected that more events lead to a more optimal alignment between CVR and FDR—a solution with less slack。 The multiple sub-cases of Case 8 from Table   2

Figure 7。 Example of infeasible solution。 The CVRs has been recorded in a location where the sampling showed no Microphone keying。

were used to plot the improved alignment achieved through additional points and is shown in Figure 8。 Each optimiza- tion solution creates three values of the offset, S: one pushed to the left limit of feasibility, one to the right, and one balanced between left and right。 Figure 8 plots S for each of these three solutions, along with the maximum absolute value difference between S expressed as Bounds。 The plot shows that the addition of only a few points quickly causes an asymptotic convergence of the bounds of S。

Theoretical and Practical Implications

Before the dawn of solid state recorders, timebase variation was an ecological reality。 However, solid-state recorders present the possibility for near-negligible time- base variations, even below the regulatory 。125% per hour。 The benefit of the model presented herein is that it allows for discovery of an optimum solution with a timebase tolerance r 5 0。 As a ‘‘first pass’’ solution to CVR/FDR alignment, if the solution presented herein is discovered to be feasible then a minimal timebase error can be inferred with the benefit of producing error bounds based on feasibility constraints。

If an infeasible solution is discovered, then sources of error can be investigated such as analyst perception of CVR radio transmissions or FDR malfunctions。 Once these other confounding factors are eliminated as possibilities, time- base variations can be further investigated。 If the timebase is found to be suspect, then a first or higher order linear regression or piecewise spline can be used to fit the CVR to the FDR events。

Real world considerations of CVR and FDR forensic analysis introduce challenges that influence the use of the model。 The data formats of the CVR and FDR events are qualitatively and quantitatively different。 CVR events are determined by analyst audio review of recorded information

Figure 8。 Benefit of additional points on  solution。

aided by visual representations of the waveform。 This is an inherently qualitative exercise。 Further, the CVR events are inherently event orientated—a radio transmission has a start and end time。 Conversely, FDR events are inherently quantitative and stateless。 The FDR does not directly record radio transmissions, rather it samples when a microphone keying is in the transmit or non-transmit state。

The different sources of the CVR and FDR data present a data conversion challenge。 FDR Microphone keying data is a series of bits recorded every second in FDR relative units。 CVR transmissions are start and stop events, either recorded in seconds or in traditional hour:minute:second format。 In order to use the model presented herein, the FDR binary data must be converted into events, and the CVR data into seconds and fractions thereof; this data conversion step may require custom programming。