Development of Analysis Methods Using Recent Data (2012)

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16 Analyses Using Vehicle-Based Data Data Acquisition and Preparation In May and June 2008, the Virginia Tech Transportation Institute (VTTI) provided the project team with data for 33 events observed during the 100-car in-vehicle study. These data comprised time series of measurements from the in- vehicle sensors, along with the videos from the forward cam- era, for about 30 s preceding and including the crash or near-crash event. Table 3.1 lists the variables obtained. The first task after receiving these data was to review them for completeness and accuracy and flag those events for which the data were either incomplete or problematic. For this task, a MATLAB-based graphical browsing tool was developed that loaded the data from the VTTI-provided text file, allowing the analyst to plot the history of selected mea- surements and to perform two initial simulations of the tra- jectory of the instrumented vehicle, using either speed- or acceleration-based measurements as input. Inconsistencies between the outputs of these two models would then indicate problems with either the speed or the acceleration data (or possibly both) for that event. For five of the events, measurements from the forward radar were not available, so for these it was not possible to reconstruct the actions of the leading vehicle. For several more of the events, there was a clear discrepancy between the trajec- tory of the instrumented vehicle as indicated by the speedom- eter, heading, and yaw measurements, and the trajectory reconstructed from the acceleration measurements, indicat- ing that caution should be used when using these data. For the instrumented vehicle, the data available consisted of speedometer output, lateral and longitudinal accelera- tions, yaw, heading, and indications of the status of the turn signal, the brake, and the accelerator, recorded at 10 Hz. For the lead vehicle, the available data consisted of range, range rate, and azimuth obtained from the forward-viewing radar, also recorded at 10 Hz. Latitude and longitude values from the GPS receiver were available, but in all cases these values were essentially constant throughout the event. After initial examination of the data obtained for each of the 33 cases, a summary was prepared (see Table 3.2) identify- ing the potential cases that could be examined for this research, based on the quality and the completeness of the available data. Several of the events involved lane-changing, swerving, or merging on the part of one of the involved vehicles, so that the forward radar of the instrumented vehicle provided only limited information about the leading vehicle. In total, seven of the 33 events were analyzed. Those seven cases are 99540, 104119, 73082, 104851, 104283, 60289, and 92660. In the following sections, the analysis of each of these seven events is described. The accuracy of the conclusions, though, depends on the accuracy of the data on which they are based. Although the project team is confident that the results are consistent with the data provided, these analyses are pre- sented as examples of what could potentially be accomplished using vehicle-based field data rather than as final determina- tions of what truly happened in these events. Case 99540 Description from video: Figures 3.1–3.3 illustrate that in this event, the instrumented (i.e., following) vehicle is traveling in the right-hand lane of a multilane highway and exits this highway to the right. The exit ramp connects to another multi- lane highway, and the leading vehicle slows and then comes to a stop at the merge point. The following vehicle collides with the lead vehicle, which moves forward and then stops on the roadway’s shoulder. Approximately 35 s of data were available from the instru- mented vehicle at 10 Hz. These data included speeds from the instrumented vehicle’s speedometer, and range and range rate from its forward radar, as shown in Figure 3.4. In addition to the original data, approximate speeds for the leading vehicle were computed by adding the instrumented C h A P t e r 3

17 Table 3.1. Data Obtained from 100-Car In-Vehicle Study Data Requested Data Delivered Notes Units Sync frames Speed Speed mile/hr GPS location lat, lon degrees/s Throttle Throttle unitless Brake brake_onoff 0 = off, 1 = on Lateral acceleration accel_x g Longitudinal acceleration accel_y g Target ID fwd_ID_n n = 1,2, . . . 7 cycles 1-255 Range fwd_range_n n = 1,2, . . . 7 ft Range-rate fwd_range_rate_n n = 1,2, . . . 7 ft/s Azimuth fwd_azimuth_n n = 1,2, . . . 7 degrees Yaw Yaw degrees/s Turn signal state turn_signal 0 = off; 1 = left; 2 = right; 3 = both Video forward Video forward avi format. Video is not synchronized with parametric data. Table 3.2. Summary of the Data Obtained from 33 Events Event ID Event Type Speedometer Forward Radar 04 Rear-end crash Cuts out ~4 seconds before crash 20 Rear-end crash Nonzero after video indicates vehicle stopped OK 24 Swerve to pole crash Possible Only prior to swerve 104119 Rear-end conflict OK OK 104283 Stationary lead vehicle OK OK 104851 Rear-end conflict OK OK 113846 Lane change conflict Reads constant 118405 Rear-end conflict Reads constant 135941 Merging conflict No near lead vehicle 139130 Multiple crash 167847 Evasive swerve 179442 Rear-end conflict Corrupted 180462 Rear-end conflict Corrupted 183129 Merging conflict 189066 Rear-end conflict Corrupted 20993 Rear-end conflict Reads constant 24523 Lane-change conflict After start of evasive action 38499 Rear-end crash Positive range during/after crash 40003 Rear-end crash Reads constant 0 52243 Rear-end conflict Corrupted (continued on next page)

18 estimates for each vehicle’s initial speed, the time points at which each driver changed acceleration and the corre- sponding accelerations were computed using WinBUGS, and the results are displayed in Table 3.3. For this case, because the data acquisition began after the leading driver had begun his or her final deceleration, the follower’s reac- tion time was computed as the difference between when the lead vehicle came to a stop and when the following driver initiated the final deceleration. At the time the forward radar acquired the leading vehicle, the driver of the instrumented vehicle was traveling at about vehicle’s speedometer speed to the forward radar’s range rate. The speeds for the two vehicles are displayed in Figure 3.5. Exploratory modeling for both vehicles was conducted using MATLAB. For the following (instrumented) vehicle, a three-stage model was fit, where a period of initial decel- eration lasting about 2 s was followed by a period of gentler deceleration, which was followed by a short period of much stronger deceleration starting less than 1 s before the colli- sion. For the leading vehicle, a two-stage model was fit, where roughly 2 s of deceleration was followed by a period of being stopped, which lasted until the collision. Bayes Figure 3.1. An initial view from instrumented vehicle’s forward camera (Case 99540). Figure 3.2. View as the instrumented vehicle exits (Case 99540). The leading vehicle is visible on the exit ramp. Event ID Event Type Speedometer Forward Radar 60289 Rear-end conflict OK OK 73082 Rear-end conflict OK OK 86319 Rear-end conflict Reads constant corrupted 86535 Evasive swerve conflict 87089 Rear-end crash Available only ~2 seconds before crash 92660 Evasive swerve conflict OK, done (without counterfactual) Limited 99129 Evasive swerve conflict 99540 Rear-end crash OK OK 122474 Rear-end conflict Missing 151062 Merging conflict Missing 1984 Rear-end crash Missing 3188 Merging conflict Missing 3336 Merging conflict Missing Boldface: Analyzed events. Table 3.2. Summary of the Data Obtained from 33 Events (continued)

19 14.75 ft/s, while the driver of the leading vehicle was traveling at about 8.9 ft/s. The leading driver was decelerating at about -3.7 ft/s2 and came to a stop about 2.4 s after the acquisition. The driver of the following vehicle was initially decelerating at about -2.9 ft/s2, but after about 1.9 s eased up to about -0.5 ft/s2. About 2.37 s after the leading vehicle came to a stop, the driver of the following vehicle began braking at about -12.6 ft/s2, but this was not sufficient to prevent a collision. At the time the lead vehicle came to a stop, the following vehicle was about 20.7 ft behind and traveling at about 9 ft/s. Figure 3.6 shows the speedometer speeds for the instru- mented vehicle, along with the speed history predicted by the model. Allowing for the piecewise constant nature of the recorded speedometer output, the model gives a reasonable representation of the follower’s speed profile. Figure 3.7 shows the radar-measured range between the leading and following vehicle, along with the range predicted by the model. Again, the model gives a reasonable representation of the data. Figure 3.3. View at the time of collision with the leading vehicle (Case 99540). Figure 3.4. Speed, range, and range-rate data (Case 99540). 0 5 10 15 20 25 30 35 40 0 1 2 3 4 5 6 Time in sec feet -15 -10 -5 0 5 10 15 20 feet/sec range in feet range rate in feet/sec speed in feet/sec Figure 3.5. Speeds for leading and following vehicles (Case 99540). -4 -2 0 2 4 6 8 10 12 14 16 0 1 2 3 4 5 6 Time in sec Speed feet/sec instrumented vehicle lead vehicle

20 Table 3.3. WinBUGS Estimates for the Model Parameters for Case 99540 Variable Mean Standard Deviation 2.5%ile 97.5%ile Following Vehicle Initial speed (ft/s) 14.75 0.16 14.45 15.08 First acceleration (ft/s2) -2.87 0.14 -3.18 -2.61 Second acceleration (ft/s2) -0.48 0.08 -0.63 -0.32 Third acceleration (ft/s2) -12.57 2.31 -17.25 -8.10 First change (s) 1.94 0.09 1.75 2.12 Second change (s) 4.78 0.03 4.71 4.83 Reaction time (s) 2.37 0.12 2.13 2.59 Speed start reaction (ft/s) 8.96 0.11 8.75 9.18 Separation start reaction (t) 20.74 1.01 18.81 22.64 Leading Vehicle Initial speed (ft/s) 8.94 0.44 8.11 9.81 First acceleration (ft/s2) -3.72 0.35 -4.45 -3.085 Stop time (s) 2.41 0.12 2.20 2.59 0 2 4 6 8 10 12 14 16 0 1 2 3 4 5 6 Time in sec Speed feet/sec Measured Predicted Figure 3.6. Measured and modeled following vehicle speeds (Case 99540). Figure 3.7. Measured and modeled range data (Case 99540). 0 5 10 15 20 25 30 35 40 0 1 2 3 4 65 Time in sec Range in feet Measured Predicted

21 leader braked to a stop, as did the follower, without colliding (Figures 3.9–3.11). Approximately 35 s of data were available at 10 Hz, includ- ing speedometer-measured speeds for the instrumented vehicle and range and range rate from the follower’s forward radar. It was possible to reliably identify the lead vehicle in the radar data for about 16 s, and the speed, range, and range rate for the period are displayed in Figure 3.12. Figure 3.13 compares the speed trajectories of the leading and following vehicles. Exploratory modeling for both vehicles was conducted using MATLAB. For the following (instrumented) vehicle, a two- stage model was fit, where a period of initial acceleration was To assess the avoidability of this crash, probabilities of col- lision were computed as a function of counterfactual final decelerations on the part of the following driver, as displayed in Figure 3.8. For this event, because the following driver did not initiate evasive action until close to collision, even fairly high counterfactual decelerations are not sufficient to prevent the collision. Case 104119 Description from video: In this event, the instrumented (i.e., following) vehicle was traveling on a signalized roadway and turned left at an intersection following the lead vehicle. The Figure 3.8. Counterfactual model (Case 99540). Probability of crash Deceleration (feet/sec2) 0.9 1 0.8 0.7 0.6 0.5 0.4 0.3 -35 -30 -25 -20 -15 -10 -5 0 Figure 3.9. View at end of follower’s left turn (Case 104119). Figure 3.10. View at approximately when leader began stopping (Case 104119).

22 after about 10.6 s from the start of the data series, the leader began decelerating at about -11.94 ft/s2, which continued until the vehicle stopped. About 11.15 s from the start of the data series, the follower began decelerating at about -9.47 ft/s2. At the time the leader began final deceleration, the follower was about 20.7 ft behind and traveling at about 36 ft/s. The follow- er’s reaction time was fairly quick, about 0.53 s. Figure 3.14 compares the following vehicle’s speed as given by its speedometer and as predicted by the fitted model. Figure 3.15 shows a similar comparison of the range between the follower and leader as given by the forward radar and the range as predicted by the trajectory models. In both cases, there is a plausible reconstruction of the data series. Finally, Figure 3.16 displays the probability of a rear-end crash occurring as a function of counterfactual final decelera- tions on the part of the following driver. Case 73082 Description from video: In this event, both the leading and the following vehicles are initially stopped at a signalized inter- section. The lead vehicle accelerates, then the follower acceler- ates and the leader pulls away from the follower. The leader then brakes to a stop, as does the follower, and the follower stops short of the leader without colliding (Figures 3.17–3.19). Figures 3.20 and 3.21 show the speed, range, and range- rate plots of the following and leading vehicles. Exploratory modeling suggested a three-stage model for the following vehicle and a four-stage model for the leader. Bayes estimates for each vehicle’s initial speed, the time points at which each driver changed acceleration, and the corre- sponding accelerations were computed using WinBUGS. followed by deceleration to a stop. For the leading vehicle, a three-stage model was fit, where a first stage of acceleration was followed by a stage of gentler acceleration, which was then fol- lowed by decelerating to a stop. Bayes estimates for each vehi- cle’s initial speed, the time points at which each driver changed acceleration, and the corresponding accelerations were com- puted using WinBUGS. The results are displayed in Table 3.4. The following driver’s reaction time was determined as the dif- ference between when the follower began final deceleration and when the leader began final deceleration. In this case, at the time of the start of the data series, the lead- ing vehicle was traveling at about 18.9 ft/s and accelerating at about 3.34 ft/s2, while the follower was traveling at about 20.6 ft/s and accelerating at about 1.45 ft/s2. After about 3.46 s, the leader eased his or her acceleration to about 0.62 ft/s2, and Figure 3.11. View when follower stopped (Case 104119). Figure 3.12. Speed, range, and range-rate data (Case 104119). -10 0 10 20 30 40 50 0 42 6 8 10 12 14 16 18 Time in sec feet -20 -10 0 10 20 30 40 feet/sec range in feet range rate in feet/sec speed in feet/sec Note: Discontinuities are due to missing data.

23 leader increased the deceleration rate to about -13.5 ft/s2. The following driver initially accelerated at about 5.4 ft/s2, and after about 6.65 s, eased to about 2.0 ft/s2. After about 12 s, the follower began braking at the relatively high rate of -18.3 ft/s2. The follower did not appear to have responded to the leader’s initial deceleration. Figure 3.22 compares the following vehicle’s speed as given by its speedometer and the speed as predicted by the fitted model. Figure 3.23 shows a similar comparison of the range between the follower and leader as given by the These results are displayed in Table 3.5. The following driver’s reaction time was determined as the difference between the time when the follower’s final deceleration began and the time when the leader’s final deceleration began. For this case, the follower’s initial speed was taken to be known and equal to 0 ft/s, while at the start of the data sequence the leader was traveling at about 2.15 ft/s and accel- erating at 10.1 ft/s2. After about 1.8 s, the leader reduced acceleration to about 4.1 ft/s2. After about 8.8 s the leader began decelerating at -3.9 ft/s2, and after about 10.2 s, the Figure 3.13. Speeds of leading and following vehicles (Case 104119). -10 0 10 20 30 40 0 5 10 15 20 Time in sec Speed feet/sec instrumented vehicle lead vehicle Note: Discontinuities are due to missing data. Table 3.4. WinBUGS Estimation Summary for Case 104119 Variable Mean Standard Deviation 2.5%ile 97.5%ile Following Vehicle Initial speed (ft/s) 20.6 0.24 20.1 21.0 First acceleration (ft/s2) 1.45 0.04 1.38 1.54 Second acceleration (ft/s2) -9.47 0.21 -9.89 -9.05 First change (s) 11.15 0.06 11.04 11.26 Reaction time (s) 0.53 0.04 0.45 0.62 Speed start reaction (ft/s) 36.04 0.23 35.6 36.5 Separation start reaction (ft) 20.74 1.01 18.81 22.64 Leading Vehicle Initial speed (ft/s) 18.92 0.31 18.3 19.52 First acceleration (ft/s2) 3.34 0.14 3.08 3.62 Second acceleration (ft/s2) 0.62 0.05 0.51 0.72 Third acceleration (ft/s2) -11.94 0.32 -12.58 -11.34 First change (s) 3.47 0.13 3.22 3.73 Second change (s) 10.61 0.05 10.51 10.72

24 Figure 3.14. Measured and modeled following vehicle speeds (Case 104119). 0 5 10 15 20 25 30 35 40 0 5 10 15 20 Time in sec Speed feet/sec Measured Predicted Figure 3.15. Measured and modeled range data (Case 104119). 0 5 10 15 20 25 30 35 40 45 50 0 2 4 6 8 10 12 14 Time in sec Range in feet Measured Predicted Figure 3.16. Counterfactual model (Case 104119). 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -32 -27 -22 -17 -12 -7 -2 Probability Deceleration (feet/sec2)

25 forward radar and the range as predicted by the trajectory models. In both cases, there is a plausible reconstruction of the data series. Case 104851 In this case, the instrumented vehicle (i.e., the following vehi- cle) at the start of the video (see Figure 3.24) took a right turn and continued to follow the leading vehicle. But then the leading vehicle decelerated and came to a complete stop. This forced the following vehicle also to decelerate, resulting in a near crash. However, the following driver’s deceleration was sufficient to enable the vehicle to come to a complete stop without any collision. Although the total length of the video was 19 s, the event actually happened within the first 8 s. In the remaining period of time, both vehicles were stopped. Figure 3.19. Following vehicle stopped behind leader (Case 73082). Figure 3.17. Both vehicles in initial stopped position (Case 73082). Figure 3.18. Lead vehicle begins braking (Case 73082). The leading vehicle came to a complete stop, indicated by the brake lights, which almost resulted in a rear-end collision. Figure 3.25 shows the speed trajectories of the leading and following vehicles. The blue and red lines indicate the speed of the following and leading vehicles in ft/s. The speed of the following vehicle was obtained directly from the speedometer of the instrumented car. The approxi- mate speed of the leading vehicle was calculated by adding the speed of the following vehicle and the range-rate data obtained from radar. A similar approach was adopted for all the remaining cases discussed in this section. Figure 3.26 shows the range and range-rate data obtained for this event. After initial estimates of the change points and accelera- tions were obtained from MATLAB, the trajectory model was fitted in WinBUGS for final estimates. In this case, a three- stage model was developed for the following vehicle, with ini- tial acceleration followed by two different deceleration stages. Table 3.6 gives the final MCMC simulation estimates of the parameters. When the radar acquired the leading vehicle, the initial speeds of the following and leading vehicles were 25.66 ft/s and 26.07 ft/s, respectively. The leading vehicle decelerated in three different stages. The first two deceleration stages were characterized by mild deceleration followed by a very steep deceleration (–24.29 ft/s2), bringing the leading vehi- cle to a complete stop. Subsequently, the following vehicle initially was accelerating for 2.626 s, and then it decelerated at –21.76 ft/s2 followed by a third deceleration of –2.87 ft/s2. The predicted piecewise acceleration model was compared by fitting the observed data. The range and speed of the following vehicle was fitted as shown Figures 3.27 and 3.28. Table 3.6 lists the estimates obtained from the WinBUGS output.

26 Respective speed trajectories for the leading and following vehicles were plotted in Figure 3.33. The radar could only man- age to capture the leading vehicle’s information for about 5 s. Also, the range and range-rate data were collected as shown in Figure 3.34. Initial speed of the following vehicle was 60 ft/s, compared to the initial speed of 30.93 ft/s for the leading vehicle (Table 3.7). This speed is the estimated speed of the leading vehicle when the radar captured information about the lead- ing vehicle for the first time. A two-stage model was proposed for the following vehicle where in the first stage the vehicle decelerated at -7.57 ft/s2 until 3.92 s, then shifted to a stron- ger deceleration rate of -16.16 ft/s2. The leading vehicle’s tra- jectory was also fitted with a two-stage model, with -10 ft/s2 of deceleration in the first stage for 1.714 s, and -4.332 ft/s2 deceleration in the second stage. Similar to the previous cases, a counterfactual model based on different deceleration rates for the following vehi- cle was simulated, and for each deceleration, a probability of crash was computed. Figure 3.29 shows how the chance of crash varies over different counterfactual deceleration values. Case 104283 This event, as shown in Figures 3.30–3.32, is a near crash. The instrumented vehicle was traveling in the rightmost lane of an arterial and continued to travel until it was forced to a complete stop to avoid a rear-end collision with the leading vehicle, which was waiting for a gap to change lanes at a merging section of the arterial. The total duration of the video was 35 s, and the event occurred at about 23 s. Figure 3.21. Speeds of leading and following vehicles (Case 73082). 0 10 20 30 40 50 60 0 5 10 15 Time in sec Speed feet/sec following vehicle leading vehicle 0 10 20 30 40 50 60 70 80 0 5 10 15 Time in sec feet -30 -20 -10 0 10 20 30 40 50 60 feet/sec range in feet following vehicle speed in feet/sec range rate in feet/sec Figure 3.20. Speed, range, and range-rate data (Case 73082).

27 Figure 3.22. Measured and modeled speedometer speeds from following vehicle (Case 73082). 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 Time in sec Speed feet/sec Measured Predicted Table 3.5. Bayes Estimation Summary for Case 73082 Variable Mean Standard Deviation 2.5%ile 97.5%ile Following Vehicle Initial speed (ft/s) 0 — — — First acceleration (ft/s2) 5.41 0.03 5.34 5.47 Second acceleration (ft/s2) 2.0 0.12 1.74 2.23 Third acceleration (ft/s2) -18.33 0.41 -19.16 -17.51 First change (s) 6.65 0.09 6.485 6.84 Second change (s) 11.96 0.05 11.86 12.05 Reaction time (s) 1.75 0.12 1.50 2.0 Speed start reaction (ft/s) 43.08 0.37 42.37 43.78 Separation start reaction (ft) 74.05 0.19 73.61 74.37 Leading Vehicle Initial speed (ft/s) 2.15 0.23 1.715 2.56 First acceleration (ft/s2) 10.1 0.26 9.64 10.59 Second acceleration (ft/s2) 4.07 0.05 3.97 4.18 Third acceleration (ft/s2) -3.87 0.74 -5.36 -2.46 Fourth acceleration (ft/s2) -13.52 0.41 -14.41 -12.76 First change (s) 1.82 0.06 1.69 1.93 Second change (s) 8.77 0.09 8.61 8.96 Third change (s) 10.21 0.09 10.03 10.39

28 The piecewise model appears plausible as shown in Fig- ures 3.35 and 3.36 fitting the observed speed of the follow- ing vehicle and range data. Also, a counterfactual model (see Figure 3.37) was devel- oped that shows that if everything else remained constant but the deceleration of the following vehicle in the last stage was stronger than -5.7 ft/s2, then the probability of a crash is essentially zero; on the other hand, if the deceleration was weaker than about -4.2 ft/s2, a crash is nearly certain. Case 60289 As shown in Figure 3.38, in this event the two vehicles were closely following each other. The leading vehicle accelerated and then traveled at uniform speed before it decelerated to almost zero speed. The following vehicle kept to the same pat- tern as the leading vehicle, shown in Figure 3.39. Range and range-rate data obtained from the radar is shown in Figure 3.40. A four-stage model was constructed to fit the following vehicle’s speed trajectory. Initially, the following vehicle was traveling at 11.21 ft/s and then accelerated at 3.15 ft/s2 for 5.36 s. Then it traveled at almost constant speed for another 5 s before decelerating at -2.419 ft/s2 for 4.3 s, followed by a strong deceleration of -10.74 ft/s2, and finally came to a stop at 16.47 s. A similar pattern was observed for the leading vehicle, which had an initial acceleration stage of 8.16 ft/s2 for 1.764 s, followed by a period of 8.277 s of almost constant speed, and then two deceleration stages, with the final deceleration rate as high as -9.502 ft/s2. The similar speed profile of the two vehi- cles seems reasonable because they were following each other closely in this case. Table 3.8 shows the WinBUGS estimates. Predicted versus observed speed and range values (see Fig- ures 3.41 and 3.42) were plotted and look quite reasonably represented by the four-stage model. A similar counterfactual model (see Figure 3.43) was devel- oped to show the probability of a crash for different decelera- tion values in the final stage of the following vehicle. Case 92660 In this event, a vehicle was closely following another vehicle on a two-lane, two-way highway as shown in Figure 3.44. The leading vehicle suddenly stopped, and the following vehicle had to swerve to avoid a collision, as shown in Figure 3.45. The speed trajectory (see Figure 3.46) shows that the leading vehicle initially traveled at mild acceleration for a considerable period of time followed by a steep deceleration, which intensi- fied in the last or final phase. On the other hand, the following (instrumented) vehicle started with a gentle acceleration and Figure 3.23. Measured and modeled range data for leading vehicle (Case 73082). 0 10 20 30 40 50 60 70 80 0 5 10 15 Time in sec Range feet Measured Predicted Figure 3.24. View of the leading vehicle (Case 104851).

29 Figure 3.25. Speed trajectories of the leading and following vehicles (Case 104851). Time in sec 6 Figure 3.26. Range and range-rate data (Case 104851). 0 5 10 15 20 25 30 35 0 21 3 4 Time in sec -16 -14 -12 -10 -8 -6 -4 -2 0 Range rate feet/sec range range rate Range in feet

30 Table 3.6. WinBUGS Estimates for the Model Parameters for Case 104851 Variable Mean Standard Deviation 2.50% Median 97.50% Following Vehicle Initial speed (ft/s) 25.66 0.3869 24.92 25.66 26.45 First acceleration (ft/s2) 1.567 0.2429 1.072 1.566 2.027 Second acceleration (ft/s2) -21.76 0.7101 -23.06 -21.79 -20.3 Third acceleration (ft/s2) -2.876 0.3197 -3.461 -2.891 -2.212 First change (s) 2.626 0.02057 2.572 2.629 2.657 Second change (s) 3.811 0.03753 3.755 3.806 3.891 Reaction time (s) 1.059 0.04373 0.9932 1.052 1.161 Leading Vehicle Initial speed (ft/s) 26.07 0.4079 25.27 26.07 26.88 First acceleration (ft/s2) -2.973 0.2788 -3.54 -2.971 -2.434 Second acceleration (ft/s2) -6.172 0.4611 -7.155 -6.153 -5.319 Third acceleration (ft/s2) -24.29 0.7389 -25.61 -24.34 -22.71 First change (s) 2.752 0.02641 2.674 2.755 2.793 Second change (s) 3.362 0.01218 3.339 3.361 3.387 Figure 3.27. Predicted and observed range data (Case 104851). 0 5 10 15 20 25 30 35 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 3.3 3.6 Time in sec Range in feet Observed Predicted Figure 3.28. Predicted and observed instrumented speeds (Case 104851). 0 5 10 15 20 25 30 35 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Time in sec Speed feet/sec Predicted Observed

31 Figure 3.29. Counterfactual model (Case 104851). 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -10 -8 -6 -4 -2 0 Probability Deceleration (feet/sec2) Figure 3.30. Initial view from the instrumented vehicle traveling in the rightmost lane (Case 104283). Figure 3.31. View near the merging section, with leading vehicle waiting for a gap (Case 104283). then moved at almost constant speed for some time, followed by the final deceleration as a reaction to the leading vehicle’s behavior. Range and range-rate data are shown in Figure 3.47. The video shows that the following vehicle had to swerve around the lead vehicle to avoid a crash, which suggests a two- dimensional analysis. The focus here, however, is to extract as much information as possible from a one-dimensional approach. Table 3.9 lists the WinBUGS estimates for the parame- ters. A three-stage model was developed for both the lead- ing and the following vehicles. The most highlighted result that can be seen from the estimates is the very strong decel- eration in the final stage. The leading vehicle had an initial speed of 40 ft/s and accelerated gently at 0.5 ft/s2 for 7 s before decelerating at -14.76 ft/s2 for approximately 2.3 s, followed by a more intense deceleration of -23 ft/s2 and finally stop- ping. The following vehicle, with an initial speed of 33.75 ft/s, accelerated at 2.48 ft/s2 for 4.23 s and then moved at almost zero acceleration for another 4.5 s before finally decelerating at -15.57 ft/s2. Figure 3.48 shows the predicted and observed range values. The counterfactual model for this case study is not shown because the following vehicle, aside from decelerating, swerved to avoid the crash.

32 Figure 3.33. Speed trajectories for the leading and following vehicles (Case 104283). 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 Time in sec Speed feet/sec following vehicle leading vehicle Figure 3.34. Range and range-rate data (Case 104283). 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 Time in sec feet -40 -35 -30 -25 -20 -15 -10 -5 0 feet/sec range in feet range rate in feet/sec Figure 3.32. Following vehicle just managed to stop, resulting in a near-crash scenario (Case 104283).

33 Table 3.7. WinBUGS Estimates for Case 104283 Variable Mean Standard Deviation 2.50% Median 97.50% Following Vehicle Initial speed (ft/s) 60.12 0.3074 59.54 60.12 60.74 First acceleration (ft/s2) -7.574 0.1257 -7.821 -7.573 -7.333 Second acceleration (ft/s2) -16.16 0.372 -16.86 -16.17 -15.41 First change (s) 3.922 0.04541 3.823 3.929 3.991 Time when stop (s) 5.805 0.027 5.754 5.804 5.861 Reaction time (s) 2.207 0.0607 2.083 2.209 2.322 Leading Vehicle Initial speed (ft/s) 30.93 0.437 30.12 30.91 31.81 First acceleration (ft/s2) -10.86 0.3323 -11.57 -10.84 -10.26 Second acceleration (ft/s2) -4.332 0.1572 -4.648 -4.331 -4.03 First change (s) 1.714 0.05528 1.602 1.716 1.816 Time when stop (s) 4.559 0.07132 4.424 4.557 4.704 Figure 3.35. Predicted and observed instrumented speeds (Case 104283). 0 10 20 30 40 50 60 70 0 0.8 1.6 2.4 3.2 4.0 4.8 5.6 Time in sec Speed feet/sec Predicted Observed Figure 3.36. Predicted and observed range values (Case 104283). Range in feet 0 50 100 150 200 0 0.8 1.6 2.4 3.2 4.0 4.8 5.6 Time in sec Observed Predicted

34 Figure 3.38. Initial view of the leading vehicle (Case 60289). Figure 3.37. Counterfactual model (Case 104283). 0 0.2 0.4 0.6 0.8 1 1.2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 Probability Deceleration (feet/sec2)

35 Figure 3.39. Speed trajectories of the leading and following vehicles (Case 60289). Figure 3.40. Range and range-rate data (Case 60289). 0 5 10 15 20 25 30 35 40 45 50 0 2 4 6 8 10 12 14 Time in sec feet -10 -5 0 5 10 15 feet/sec range in feet range rate in feet/sec

36 Figure 3.41. Predicted and observed instrumented speeds (Case 60289). Table 3.8. WinBUGS Estimates for Case 60289 Variable Mean Standard Deviation 2.50% Median 97.50% Following Vehicle Initial speed (ft/s) 11.21 0.2399 10.74 11.21 11.67 First acceleration (ft/s2) 3.149 0.06246 3.034 3.146 3.275 Second acceleration (ft/s2) 0.7217 0.03928 0.6431 0.7219 0.7981 Third acceleration (ft/s2) -2.419 0.1075 -2.635 -2.415 -2.22 Fourth acceleration (ft/s2) -10.74 0.3316 -11.38 -10.74 -10.07 First change (s) 5.364 0.06755 5.236 5.362 5.495 Second change (s) 10.71 0.05586 10.61 10.71 10.83 Third change (s) 14.3 0.03184 14.23 14.3 14.36 Time when stopped (s) 16.47 0.05112 16.37 16.47 16.57 Reaction time (s) 0.4847 0.04604 0.3996 0.4829 0.5788 Leading Vehicle Initial speed (ft/s) 14.07 0.3193 13.46 14.07 14.71 First acceleration (ft/s2) 8.16 0.2434 7.679 8.164 8.631 Second acceleration (ft/s2) -0.00214 0.04673 -0.09826 -0.00121 0.08024 Third acceleration (ft/s2) -1.45 0.07088 -1.591 -1.448 -1.312 Fourth acceleration (ft/s2) -9.502 0.3231 -10.12 -9.506 -8.857 First change (s) 1.764 0.03767 1.69 1.763 1.841 Second change (s) 8.277 0.1001 8.073 8.28 8.461 Third change (s) 13.81 0.03837 13.74 13.81 13.88

37 Figure 3.44. Initial view of the leading vehicle on a two-lane, two-way highway (Case 92660). Figure 3.45. Instrumented vehicle swerved to avoid collision (Case 92660). Figure 3.42. Predicted and observed range values (Case 60289). Time in sec Predicted Observed Range in feet Figure 3.43. Counterfactual model (Case 60289). 0 0.2 0.4 0.6 0.8 1 1.2 -32 -27 -22 -17 -12 -7 -2 3 Probability Deceleration (feet/sec2)

38 Figure 3.47. Range and range-rate data (Case 92660). 0 10 20 30 40 50 60 0 2 6 4 8 10 Time in sec -35 -30 -25 -20 -15 -10 -5 0 5 10 Range rate feet/sec range range rate Range feet Figure 3.46. Speed trajectories of the leading and following vehicles (Case 92660).

39 Table 3.9. WinBUGS Estimates for the Parameters for Case 92660 Variable Mean Standard Deviation 2.50% Median 97.50% Following Vehicle Initial speed (ft/s) 33.75 0.2246 33.33 33.74 34.2 First acceleration (ft/s2) 2.479 0.07467 2.332 2.48 2.625 Second acceleration (ft/s2) 0.1819 0.08929 0.01293 0.1802 0.3597 Third acceleration (ft/s2) -15.57 0.8826 -17.29 -15.57 -13.83 First change (s) 4.229 0.09666 4.036 4.232 4.407 Second change (s) 8.73 0.04538 8.635 8.734 8.812 Time when stop (s) 11.62 0.1311 11.38 11.61 11.9 Leading Vehicle Initial speed (ft/s) 40.98 0.2145 40.58 40.98 41.41 First acceleration (ft/s2) 0.504 0.05306 0.3998 0.506 0.6038 Second acceleration (ft/s2) -14.76 0.4033 -15.55 -14.76 -13.98 Third acceleration (ft/s2) -23.62 3.443 -31.91 -23.15 -18.31 First change (s) 7.004 0.03893 6.928 7.005 7.077 Second change (s) 9.269 0.1305 9.003 9.267 9.51 Figure 3.48. Predicted and observed range values (Case 92660).