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40 C h a p t e r 4 Data acquisition and preparation The locations selected for analyses of site-based video data were two freeway segments on westbound Interstate 94 near downtown Minneapolis. One is approximately 500 ft long, located between Minnesota State Highway 65 and Portland Avenue, and the other is approximately 600 ft long, located between Portland Avenue and Park Avenue South. Fig- ure 4.1 provides an overhead view of these two sites. The traffic traveling on these two segments was recorded using two cameras installed by the Minnesota Traffic Obser- vatory (MTO) on the roof of a 121-ft-high building near 3rd Avenue. The videos were transferred to the MTO and saved at a resolution of 640 Ã 480 pixels and 10 frames/s, from 11 a.m. to 8 p.m. daily. Given a target vehicle, its time-series of posi- tions expressed in screen coordinates were manually extracted frame by frame using VideoPoint software (see Figure 4.2). The screen coordinates obtained from VideoPoint were then converted to ground coordinates by first matching sev- eral reference points on the video images to corresponding points on high-resolution satellite photos and then applying standard photogrammetric methods. I-94 Case 1 Description from the video: In this event, the following vehi- cle (Vehicle 2) and leading vehicle (Vehicle 1) were traveling in the middle lane (Figures 4.3 and 4.4). Vehicle 2 collided with Vehicle 1. Trajectory data after the collision were not collected. Approximately 15 s of data were available from the video. Inspection of these data indicated that both vehicles were traveling at constant speeds approximately 9 s before the col- lision. Only the trajectory data from the last 6 s were used, and these are displayed in Figure 4.5. Exploratory modeling for both vehicles was conducted using R software. For Vehicle 1, a two-stage model was fit, where a gentle acceleration lasting about 2.7 s was followed by a stronger deceleration. For Vehicle 2, a one-stage model was fit, where a gentle acceleration lasted until the collision. Bayes estimates for each vehicleâs initial speed, the time points at which the accelerations changed, and the accelera- tions in all stages were computed using WinBUGS. These results are displayed in Table 4.1. At the beginning of the study period, Driver 2 was travel- ing at 24.21 ft/s, while Driver 1 was traveling at 27.5 ft/s. Driver 1 accelerated at 1.6 ft/s2 for about 2.7 s and then decel- erated at -8.779 ft/s2 for about 3.1 s. Driver 2 was accelerating at about 1.16 ft/s2 until the collision. No evidence from video or trajectory data showed that Driver 2 decelerated to prevent a collision. Figures 4.6 and 4.7 show the distance trajectories of Vehicles 1 and 2, along with the distance trajectories pre- dicted by the models. I-94 Case 2 Description from the video: In this event, the following vehi- cle (Vehicle 2) and leading vehicle (Vehicle 1) were traveling in the middle lane (Figures 4.8 and 4.9). Vehicle 2 collided with Vehicle 1. Approximately 4 s of data were available from the video. The trajectory data used for analysis are displayed in Figure 4.10. Exploratory modeling for both vehicles was conducted using R software. For Vehicle 1, a two-stage model was fit, where a strong deceleration lasted about 1.5 s and was fol- lowed by a less strong deceleration. For Vehicle 2, a one-stage model was fit, where a gentle acceleration lasted until the col- lision. Bayes estimates are displayed in Table 4.2. At the beginning of the study period, Driver 2 was travel- ing at 33.02 ft/s, while Driver 1 was traveling at 33.12 ft/s. Analyses Using Site-Based Video Data (text continues on page 44)
41 Figure 4.4. View at the time of collision (I-94 Case 1).Figure 4.3. View at the time the two vehicles enter the study segment (I-94 Case 1). Figure 4.2. Illustration of VideoPoint trajectory extraction. Study Sites I 94 I 35W Figure 4.1. Satellite view of two distance-based trajectory-data-collection sites.
42 250 300 350 400 450 500 0 1 2 3 4 5 6 Time in sec feet vehicle 1 vehicle 2 Figure 4.5. Distance trajectory data (I-94 Case 1). 250 300 350 400 450 500 0 2 4 6 8 Time in sec feet Measured Predicted Figure 4.6. Measured and modeled Vehicle 1 distance trajectories (I-94 Case 1). Table 4.1. WinBUGS Estimates for I-94 Case 1 Variable Mean Standard Deviation 2.5%ile 97.5%ile Vehicle 2 (following) Initial speed (ft/s) 24.21 0.1731 23.87 24.56 First acceleration (ft/s2) 1.155 0.07787 0.9997 1.306 Vehicle 1 (leading) Initial speed (ft/s) 27.5 0.5015 26.46 28.45 First acceleration (ft/s2) 1.643 0.4585 0.8183 2.615 Second acceleration (ft/s2) -8.779 0.4278 -9.656 -7.983 First change (s) 2.663 0.1136 2.433 2.883
43 Figure 4.9. View at the time of collision (I-94 Case 2).Figure 4.8. View at the time the two vehicles enter the study segment (I-94 Case 2). 250 300 350 400 450 500 0 2 4 6 Time in sec feet Measured Predicted Figure 4.7. Measured and modeled Vehicle 2 distance trajectories (I-94 Case 1). 660 680 700 720 740 760 780 800 820 0 1 2 3 4 Time in sec feet vehicle 1 vehicle 2 Figure 4.10. Distance trajectory data (I-94 Case 2).
44 Table 4.2. WinBUGS Estimates for I-94 Case 2 Variable Mean Standard Deviation 2.5%ile 97.5%ile Vehicle 2 (following) Initial speed (ft/s) 33.02 0.2069 32.62 33.43 First acceleration (ft/s2) -2.512 0.1425 -2.793 2.231 Vehicle 1 (leading) Initial speed (ft/s) 33.12 0.8424 31.89 35.13 First acceleration (ft/s2) -10.52 1.911 -15.11 -8.507 Second acceleration (ft/s2) -5.436 0.5798 -6.377 -4.099 First change (s) 1.505 0.3309 0.8608 2.134 730 740 750 760 770 780 790 800 810 0 1 2 3 4 Time in sec feet Measured Predicted Figure 4.11. Measured and modeled Vehicle 1 distance trajectories (I-94 Case 2). Driver 1 was decelerating at -10.52 ft/s2 for about 1.5 s and then decelerated at -5.436 ft/s2 for about 2.3 s. Driver 2 was decelerating at -2.512 ft/s2 but was not able to prevent the collision. Figures 4.11 and 4.12 show the distance trajectories of Vehicles 1 and 2, along with the distance trajectory pre- dicted by the models. I-94 Case 3 Description from the video: In this event, three vehicles are traveling in the right lane of the study segment (Figures 4.13 and 4.14). Vehicle 3 collides with Vehicle 2. Approximately 7 s of data were available from the video. The trajectory data used for analysis are displayed in Figure 4.15. Exploratory modeling for each vehicle was conducted using R software. For Vehicle 1, a three-stage model was fit, where a gentle acceleration lasting for about 2.3 s was fol- lowed by a 2.4-s stronger deceleration and then by a 2.4-s gentler deceleration. For Vehicle 2, a two-stage model was fit, where a gentle deceleration lasting for about 3.5 s was followed by a 3.2-s stronger deceleration. For Vehicle 3, a three-stage model was fit. The trajectory modeling showed that Driver 3 decelerated in all three stages. Bayes estimates are displayed in Table 4.3. The reaction time of Driver 2 was calculated as the time difference between Driver 2âs first change point and Driver 1âs first change point. The reaction time of Drivers 3 was calculated as the time difference between Driver 3âs second change point and Driver 2âs first change point. At the beginning of study period, Drivers 1, 2, and 3 were traveling at 21.33 ft/s, 33.42 ft/s, and 51.29 ft/s, respectively. Driver 1 accelerated at 1.048 ft/s2 for about 2.2 s at first, then decelerated at -8.8 ft/s2 for about 2.3 s, and then decelerated at -0.8968 ft/s2 for about 2.4 s. Driver 2 was decelerating at -0.8968 ft/s2 for about 3.5 s and then decelerated at -8.0 ft/s2 for about 3.2 s. Vehicle 3 was apparently initially traveling at a much higher speed (51.29 ft/s) than the other two vehicles. (continued from page 40)
45 Figure 4.14. View at the time of collision (I-94 Case 3).Figure 4.13. View at the time the three vehicles enter the study segment (I-94 Case 3). 660 680 700 720 740 760 780 800 0 1 2 43 Time in sec feet Measured Predicted Figure 4.12. Measured and modeled Vehicle 2 distance trajectories (I-94 Case 2). 600 650 700 750 800 850 900 950 0 2 4 6 Time in sec feet Vehicle 1 Vehicle 2 Vehicle 3 Figure 4.15. Distance trajectory data (I-94 Case 3).
46 Table 4.3. WinBUGS Estimates for I-94 Case 3 Variable Mean Standard Deviation 2.5%ile 97.5%ile Vehicle 3 Initial speed (ft/s) 51.29 0.3508 50.66 52.03 First acceleration (ft/s2) -5.618 0.3798 -6.475 -4.992 Second acceleration (ft/s2) -3.206 0.2493 -3.598 -2.617 Third acceleration (ft/s2) -10.24 2.002 -14.88 -7.215 First change (s) 2.295 0.3079 1.726 2.926 Second change (s) 5.375 0.2048 4.924 5.743 Reaction time (s) 1.886 0.2197 1.412 2.285 Vehicle 2 Initial speed (ft/s) 33.42 0.1933 33.03 33.80 First acceleration (ft/s2) -0.8968 0.1368 -1.156 -0.6174 Second acceleration (ft/s2) -8.004 0.2241 -8.463 -7.576 First change (s) 3.489 0.0792 3.333 3.645 Reaction time (s) 1.231 0.1336 0.9572 1.489 Vehicle 1 Initial speed (ft/s) 21.33 0.3953 20.53 22.07 First acceleration (ft/s2) 1.048 1.048 0.2296 1.984 Second acceleration (ft/s2) -8.8 0.5076 -9.974 -7.967 Third acceleration (ft/s2) -0.9801 0.3604 -1.535 -0.1625 First change (s) 2.258 0.1116 2.046 2.49 Second change (s) 4.595 0.1188 4.353 4.819 Although Driver 3 noticed that the traffic in front was slowing down and started decelerating before entering the data-collection segment, Driver 3 was still not able to avoid collision with Vehicle 2 after decelerating at -10.24 ft/s2 for about 2.3 s in its last stage. Figures 4.16, 4.17, and 4.18 show the distance trajectories of Vehicles 1, 2, and 3, along with the distance trajectory pre- dicted by the models. In this case, to assess the avoidability of collision between Vehicles 2 and 3, probabilities of collision between these vehicles were computed as a function of counterfactual final decelerations (the third stage) of Vehicle 3. This relationship is displayed in Figure 4.19. The probability of collision between Vehicles 1 and 2 was also evaluated, assuming that Driver 2 was decelerating at dif- ferent rates in the last stage. This relationship is displayed in Figure 4.20. In this case, since the relative speed between Vehicles 1 and 2 in the last stages is small, for most counter- factual deceleration rates of Vehicle 2, the corresponding probabilities of collision are either 1 or 0. I-94 Case 4 Description from the video: In this event, three vehicles were traveling in the right lane of the study segment (Figures 4.21 and 4.22). Vehicle 3 collided with Vehicle 2. Approximately 10 s of data were available from the video. The trajectory data used for analysis are displayed in Figure 4.23. Exploratory modeling for both vehicles was conducted using R software. A three-stage model was fit to each vehicle trajec- tory. Vehicle 1 accelerated for about 2.6 s, which was followed first by a 4.1-s strong deceleration and then by a 3.7-s gentle deceleration. The behavior of Drivers 2 and 3 was almost the same as that of Driver 1 but with stronger deceleration in their last stages. The WinBUGS estimates are shown in Table 4.4. (text continues on page 51)
47 600 650 700 750 800 850 900 0 2 4 6 8 Time in sec feet Measured Predicted Figure 4.18. Measured and modeled Vehicle 3 distance trajectories (I-94 Case 3). 600 650 700 750 800 850 900 0 2 4 6 8 Time in sec feet Measured Predicted Figure 4.17. Measured and modeled Vehicle 2 distance trajectories (I-94 Case 3). 800 820 840 860 880 900 0 1 2 3 4 5 6 7 Time in sec feet Measured Predicted Figure 4.16. Measured and modeled Vehicle 1 distance trajectories (I-94 Case 3).
48 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 3 Probability Deceleration (feet/sec2) Figure 4.19. Probability of collision as a function of counterfactual final deceleration by Driver 3 (I-94 Case 3). 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 3 Probability Deceleration (feet/sec2) Figure 4.20. Probability of collision as a function of counterfactual final deceleration by Driver 2 (I-94 Case 3).
49 Figure 4.22. View at the time of collision between Vehicles 2 and 3 (I-94 Case 4). Figure 4.21. View at the time the three vehicles enter the study segment (I-94 Case 4). 50 100 150 200 250 300 350 400 450 500 0 2 4 6 8 10 Time in sec feet Vehicle 1 Vehicle 2 Vehicle 3 Figure 4.23. Distance trajectory data (I-94 Case 4).
50 Table 4.4. WinBUGS Estimates for I-94 Case 4 Variable Mean Standard Deviation 2.5%ile 97.5%ile Vehicle 3 Initial speed (ft/s) 21.94 0.164 21.61 22.25 First acceleration (ft/s2) 2.591 0.06958 2.46 2.735 Second acceleration (ft/s2) -0.8846 0.5106 -1.874 0.1521 Third acceleration (ft/s2) -12.89 3.821 -21.83 -7.752 First change (s) 5.9 0.2449 5.336 6.334 Second change (s) 8.723 0.2545 8.171 9.163 Reaction time (s) 1.112 0.2855 0.5099 1.62 Vehicle 2 Initial speed (ft/s) 25.67 0.3143 25.0 26.21 First acceleration (ft/s2) 2.514 0.2232 2.164 3.012 Second acceleration (ft/s2) -0.2509 0.2551 -0.7828 0.2243 Third acceleration (ft/s2) -10.48 0.6891 -11.95 -9.231 First change (s) 3.769 0.3356 3.092 4.372 Second change (s) 7.612 0.1186 7.382 7.847 Reaction time (s) 0.8966 0.1646 0.5863 1.223 Vehicle 1 Initial speed (ft/s) 29.41 0.5065 28.27 30.27 First acceleration (ft/s2) 2.247 0.5051 1.52 3.485 Second acceleration (ft/s2) -0.7111 0.1872 -1.073 -0.3352 Third acceleration (ft/s2) -7.312 0.306 -7.923 -6.729 First change (s) 2.625 0.3319 1.913 3.216 Second change (s) 6.715 0.1183 6.475 6.938
51 100 150 200 250 300 350 400 450 500 0 4 82 6 10 12 Time in sec feet Measured Predicted Figure 4.24. Measured and modeled Vehicle 1 distance trajectories (I-94 Case 4). 100 150 200 250 300 350 400 450 0 42 6 8 10 12 Time in sec feet Measured Predicted Figure 4.25. Measured and modeled Vehicle 2 distance trajectories (I-94 Case 4). Although Driver 3 had the strongest final deceleration (at -12.89 ft/s2) for about 1.3 s, this was not sufficient to pre- vent the collision. Figures 4.24, 4.25, and 4.26 show the distance trajectories of Vehicles 1, 2, and 3, respectively, along with the distance trajectories predicted by the models. In this case, the relationship between a counterfactual final deceleration of Vehicle 3 and the probability of collision with Vehicle 2 is displayed in Figure 4.27. The probability of colli- sion between Vehicle 1 and 2 was also evaluated, assuming Driver 2 was decelerating at a different rate in the last stage. This relationship is displayed in Figure 4.28. The reaction times of Drivers 2 and 3 were calculated as the time difference of last change points between Vehicles 2 and 1, and between Vehicles 3 and 2. At the beginning of the study period, Drivers 1, 2, and 3 were traveling at about 29.41 ft/s, 25.67 ft/s, and 21.94 ft/s, respectively. Driver 1 first accelerated at 2.247 ft/s2 for about 2.6 s, then decelerated at -0.7111 ft/s2 for about 4.1 s, and then decelerated at -7.312 ft/s2 for about 3.7 s. Driver 2 was accelerating at 2.514 ft/s2 for about 3.8 s, decelerated at -0.2509 ft/s2 for about 3.8 s, and then decelerated at -10.48 ft/s2 to avoid colliding with Vehicle 1. Driver 3 noticed the strong deceleration of Vehicle 2 in its last stage. (continued from page 46)
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -32 -27 -22 -17 -12 -7 -2 3 Probability Deceleration (feet/sec2) Figure 4.27. Probability of collision as a function of counterfactual final deceleration by Driver 3 (I-94 Case 4). 0 100 200 300 400 500 0 42 6 8 10 12 Time in sec feet Measured Predicted Figure 4.26. Measured and modeled Vehicle 3 distance trajectories (I-94 Case 4). 52 Figure 4.28. Probability of collision as a function of counterfactual final deceleration by Driver 2 (I-94 Case 4). 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) 3
