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Rear-end collisions – naturalistic driving study
Chapter 11
Rear-end collisions e naturalistic driving study Chapter outline Data Initial analysis Studied types of drivers Claiming and analyzing traffic conflicts
198 198 202
Evaluating the results Summary References
206 210 213
203
Abstract The data used in this chapter were produced by radar, accelerometer, and speedometer devices installed in SHRP2 vehicles. Considerable data pre-processing was needed. From all the trips made by the studied types of drivers, 1.4% of the trips were randomly selected to search for rear-end conflicts. The detected conflicts were analyzed with the method presented in this book. The crash estimates obtained from these conflicts were converted to rear-end crash rates and compared to the rear-end crash rates calculated for trips made by all the SHRP2 drivers of the three types. The results obtained based on conflicts and crashes compare well. This is an appealing indication of the method’s validity. Another conclusion is that instantaneous times to collision and changes in braking rates constitute sufficient basis to claim rear-end conflicts.
Chapters 9 and 10 presented the Lomax-based analysis of road near-departures and right-angle interactions. This chapter applies the method to rear-end traffic conflicts recorded during naturalistic driving. The primary focus is on demonstrating that the crash frequency estimated with traffic conflicts follows the frequency of actual crashes. The experience gained in the process is shared with the reader to help in successful application of the method to other realworld cases. The data used in this example were collected in a large research programdthe Strategic Highway Research Program 2 (SHRP2) effected between 2006 and 2015 (Blatt et al., 2015). The Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users, passed by the USA congress in 2005, authorized spending $170 million in seven years on the SHRP2, focusing on safety and three other transportation research areas. One of the objectives was to significantly enhance highway safety by improving an Measuring Road Safety with Surrogate Events. https://doi.org/10.1016/B978-0-12-810504-7.00011-2 © 2020 Elsevier Inc. All rights reserved.
197
198 Measuring Road Safety with Surrogate Events
understanding of driving behavior through a large-scale study. Campbell reported in 2012 that 23,247 drivers were on the road driving cars as part of their daily routines (Campbell, 2012). At the conclusion of the data collection phase, the database included nearly 5.5 million trips made by 3400 participant drivers. Over 4300 total years of naturalistic driving time between 2010 and 2013 produced and validated 1549 crashes (Hankey et al., 2016). Crashes were defined: “Any contact that the subject vehicle has with an object, either moving or fixed, at any speed in which kinetic energy is measurably transferred or dissipated is considered a crash” (cit. Hankey et al., 2016). Among these crashes, 234 were rear-end collisions including 119 rear-end crashes that happened when SHRP2 drivers followed other vehicles. This chapter applies instantaneous time to collision s to estimate the conditional probability of rear-end crash and the expected number of rear-end crashes in a sample of randomly selected SHRP2 drivers. The results of the analysis are compared to the number of rear-end crashes reported for all SHRP2 drivers during the SHRP2 period. The data and their preparation, analysis, results, and discussion are included.
Data Among various pieces of data collected by instrumented vehicles included in the SHRP2 database, the following data were found useful for claiming traffic conflicts: 1. Radar-measured distance (range) to the lead vehicle reported 10 times per second, 2. Accelerometer-measured longitudinal and lateral acceleration rates of the instrumented vehicle reported 10 times per second, 3. Speedometer-measured speed of the instrumented vehicle reported once every 1e2 s at irregular rates. The speed measurements were assumed accurate based on the information obtained from the Virginia Tech personnel involved in maintaining and processing the SHRP2 data. The gaps between speed measurements were filled with the speed values obtained by integrating the longitudinal acceleration rates. Any discrepancy between the speeds measured with a speedometer and the speeds derived from the acceleration rates were reconciled by adjusting the acceleration-derived speeds through shifting and scaling that minimized the discrepancy between the two measurements. After filling the gaps between the speedometer-measured speeds these speed sequences were smoothed with a moving average of five values.
Initial analysis An initial small sample of 255 trips with traffic conflicts was selected randomly to check and control the data quality and to evaluate and modify
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initially devised methods of traffic conflict detection and analysis. Trips were selected in batches from the population and checked for at least one rear-end traffic conflict with the instantaneous travel time s < 2.0 s. The selection ended when the desired number of trips with at least one traffic conflict were found. The minimum sm value was interpreted as the end of a successful response. Following the concept of generalized separation (Chapter 6), the response delay x was calculated by subtracting sm from the sc threshold: x ¼ sc sm. Fig. 11.1 presents a possible rear-end traffic conflict, which is marked with the oval shape. Time is represented by the number of video frames progressing at the frequency of 10 per second. The evasive braking is represented by the considerable longitudinal jerk, rapidly changing the deceleration rate from -1 m/s2 to -5 m/s2, and with the instantaneous time to collision s falling below 2 s. Following the recommended diagnostic analysis of Chapter 8, the log-log curves log[1 F(x)] ¼ f[log(1 þ x/sc)] calculated with the ordered response delays x were inspected to check for indication of a Lomax distribution of x. A linear relationship with a slope corresponding to parameter ek was expected. The top curve in Fig. 11.2 is the log-log curve obtained for conflicts claimed in the test trips for threshold tc ¼ 2.0 s. The curve is apparently nonlinear. The curve exhibits change in slope at log(1 þ x/sc) ¼ 0.27 and a pronounced upward curve for log(1 þ x/sc) > 0.6. Reducing threshold tc to 1.5 s (middle curve) has moved the first nonlinearity point from 0.27 to 0.07, while the upward curve still appears in a similar location. Although threshold tc set at 1.0 s has eliminated the first nonlinearity point, the upward curve remains
FIG. 11.1 Example rear-end conflict in SHARP2 data marked (inside the oval).
200 Measuring Road Safety with Surrogate Events
FIG. 11.2
Log-log curves for the test sample with the lane exit observations included.
seemingly unchanged (see Fig. 11.2). It is obvious that a long separation threshold is not the cause of the log-log curve non-linearity. Analyzing closely the data with considerable x and short sm revealed a number of rear-end interactions where the s values were not reported at the time of sm or shortly afterward. Video frames with these events revealed lead vehicles changing lanes or leaving the road. Signaling in advance the intended lane change by the lead vehicles and initiating consistent lateral movement allowed the following drivers to anticipate the clearing of the lane. This anticipation prompted the following drivers to continue closing the gap and passing the lead vehicles at short time separations. The numerical data confirmed no or gentle braking while maintaining the unchanged direction by the followers. Some drivers even slightly accelerated before passing the spot where lead vehicles left the lane. These behaviors produced short s values while the drivers kept the situation under control with neither failure nor considerable risk. Such events do not pass the condition of traffic failure and cannot be claimed as conflicts. Fig. 11.3 presents the instrumented vehicles’ speeds at the time of sm values. The cases with a disappearing lead vehicle are represented with the filled circles. Removing these events eliminated the nonlinearity problem. This is demonstrated in Fig. 11.4 with the approximately straight log-log curve for the sc threshold lower than 2.0 s. This result concluded the first phase of the analysis. In the next step, a large sample of 76,389 trips (1.4 % of all SHRP2 trips) was randomly drawn including 12,742 trips with at least one potential traffic conflict (sm <2 s). The data provided for each trip included information about the trips, drivers, and vehicles. Additional 40-second video clips were requested for periods with questionable radar, speedometer, and accelerometer data.
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2.0 1.8 1.6
Wm value (s)
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0
10
20
30 40 Speed at Wm (mi/h)
Lane Exiting
50
60
70
80
Remaining in Lane and Braking
FIG. 11.3 Minimum instantaneous time to collision observations in the test sample.
The exposure for the entire population of drivers is relevant in the scope of the study. Hence, the total number of miles driven by all the SHRP2 drivers was obtained. In addition, the crash data information was acquired for validation of the number of crashes predicted using conflicts. The safety analysis proceeded with additional quality control. The speeds of the lead vehicles were estimated by subtracting speeds of the following vehicles from the respective range rates measured with the radar. The derived new quantity helped detect cases of lead vehicles supposedly moving in the reverse direction toward the instrumented vehicles. The negative but small radar measurements between -1 m/s and 0 m/s were assumed unreliable and
FIG. 11.4 Log-log curves for the test sample after removing the lane exit observations (sc ¼ 2.0 s).
202 Measuring Road Safety with Surrogate Events
ignored. There was also a considerable number short-lived “backward motions” associated with sudden reductions in s and small sm. Inspecting the relevant video images revealed that indeed a limited number vehicles were in the field of view of radar when moving in the opposite direction on the other side of the road. In the majority of cases though, vehicles were entering gaps in front of the instrumented vehicles. During the entering maneuver, a side of the entering vehicles were exposed to the radar beams. The beams were sliding along the sides of the gap-entering vehicles backward creating an illusion of backward movement. The entering vehicles were inheriting the ID of the other vehicles in front. This continuity of ID was increasing the appearance of legitimacy of the incorrect measurements. All the cases with negative speeds of lead vehicles were excluded from the analysis. Values of sm smaller than 0.1 s, including zero, were associated with low and positive speeds and short ranges often followed by periods with missing radar readings. The first hypothesis was made that these events were safe collisionsdphysical contacts between vehicles with neither bodily injury nor reportable material damage. According to the SHRP2 definition of crash, these events should not be defined as crashes. The Virginia Tech SHRP2 team checked several identified cases to confirm that these indeed were not collisions. A plausible explanation for missing radar readings was that low relative speeds and short ranges made the radar unreliable, and this might lead to inaccurate or missing readings. The quality control phase reduced the 18,453 potential conflicts to 7,424. The data processing moved to the final phase of claiming traffic conflicts that involved drivers of studied categories, and concurrent estimation and inspection of the expected number of crashes, and log-log curves to ensure the correctness of the results. This analysis was applied to data obtained for three types of studied drivers.
Studied types of drivers Past studies indicated that young drivers were strongly overrepresented in road crashes (Scott-Parker et al., 2013). Young drivers are frequently pointed out by police officers preparing crash reports as those who caused the crashes or contributed to their occurrence. Safety experts associate the proneness of young drivers to crashes with their limited driving experience and consequently substandard driving skills. Fig. 11.4 compares crash rates by drivers of various ages. These rates account for the exposure measured with miles traveled. The predominance of young drivers age 16e25 in crash involvement is undeniable. On the other hand, the most safe drivers are of age 40e69 who are experienced and enjoy relatively good physical and mental performance. Other research studies consistently point out that female drivers tend to drive more safely than males (Moe` et al., 2015) and are involved in fewer crashes than male drivers (Padilla et al., 2018).
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The past research studies clearly indicate that among the three groups of drivers, (1) young male 16e25, (2) mature male 46e65, and (3) mature female 46e65, young males are the worst drivers while the mature females are the best. The difference between the driving performance of young males and of mature drivers is much bigger than between mature male and female drivers. Table 11.1 presents statistics of the rear-end crashes caused by the three types of drivers during the SHRP2 program. The subject drivers were in the SHRP2 instrumented vehicles and following other vehicles when colliding with the vehicles in front of them (front hit). The numbers are generally consistent with the current knowledge on the subject and specifically with the crash rates in Fig. 11.5. It should be stressed that the rear-end crash involvement rate in Fig. 11.5 includes front hits and back hits of vehicles driven by drivers in the age groups.
Claiming and analyzing traffic conflicts An important question remaining to be answered is if the proposed Lomaxbased method is able to produce rear-end crash rate estimates that are similar to the values listed in Table 11.1. To answer this question, the Lomaxbased method was applied to traffic conflicts that occurred in a small portion of the 1.4 % trips randomly selected from all the trips made during the SHRP2 program by drivers of the types listed in Table 11.1. The events with minimum ITTC values immediately followed by lane departures of lead vehicles were eliminated. Also, all events with negative speeds of lead vehicles were removed as most likely caused by entering the gaps between lead and instrumented vehicles.
TABLE 11.1 Rear-end crash counts and rates during the SHRP2 study period (SHRP2 population). Miles driven while following another vehicle (SHRP2 population exposure)
Number of rear-end crashes (front hits)
Males 16e25
2,209,414
Males 45e64 Females 45e64
Driver type
Police reportable rear-end crashes (front hits)
Count
Rate per 100 million miles of car following
31
24
1086
1,316,178
10
6
456
1,460,122
2
2
137
204 Measuring Road Safety with Surrogate Events
FIG. 11.5
Involvement of various age groups of drivers in crashes (Tefft, 2012).
Besides the central question of failure-caused small separations between road users is the inevitability of collision if no evasion action is undertaken and successfully completed. One possible approach proposed and elaborated by Saunier et al. (2010) is predicting probable movements as continuation of conflict-free behavior that mimics the lack of hazard awareness. The prediction confirms in a counterfactual way the crash potential and provides estimates of the time to collision. Another method applied here is confirming that the observed behavior indicates the presence of collision avoidance, and using the instantaneous time to collision to approximate the time to hypothetical collision. Detecting an evasive action of a driver following another car is a confirmation that the conflict was resolved most likely by the follower and was not a coincidental acceleration of the preceding car. Two conditions were used to detect evasion: (1) there is a statistically detectable (significant) jerk in the motion of the follower immediately before the shortest instantaneous time to collision sm that (2) leads to a considerable braking at a rate of at least 1.5 m/ s2. These conditions were later confirmed as producing, with other conditions, the expected trend in the results: stable estimation of the expected number of crashes for a sequence of separation thresholds. Another matter that needed attention was that of low speeds in the period preceding a potential traffic conflict. Claiming traffic conflicts even for short separations but under low speeds may produce false positives. The source of the estimation problem is two-fold. (1) Drivers moving at low speeds may perceive no considerable risk. One would rightly claim that this is consistent with no real hazard because a small relative speed at impact produces harm neither to vehicles nor to vehicle occupants. Consequently, it is difficult to claim that a safety-related failure is possible when there is no hazard. (2) Even if an impact speed is sufficiently high to expect some damage, the outcome may still be too minor to be police-reportable. The latter concern is less critical than the former concern because it can be rectified in the subsequent analysis
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by applying a discrete-outcome model to estimate the probability of policereportable outcome. Mostly due to the concern of no hazard perception among involved drivers, traffic interactions at too low speeds should be ignored to avoid falsely claimed conflicts. Speed should be sufficiently high at collision to induce a fear of collision among participating drivers. Determining the suitable threshold for impact speed above which a conflict may be claimed is similar to determining a threshold for separation. Specifically, the threshold speed can be determined as the lowest speed at which estimates of the expected crash frequency for different separation thresholds is stable. There is an important note to make. While a low separation threshold does not introduce any bias to the crash frequency estimates, a too high speed threshold leads to underestimation of the number of crashes by neglecting valid conflicts associated with potentially serious outcomes. The speed at the hypothetical collision to be considered in the expanded procedure can be estimated with the following equation: d Impact speedðtm þ sm Þ ¼ Range rateðtm Þ þ sm $ Range rateðtm Þ dt
(11.1)
where tm is the time at which s reaches the minimum value sm. Time t ¼ tm þ sm is the approximate moment when the hypothetical collision happens if sm is short and close to time to collision T. The expanded procedure applied in the presented SHRP2 study includes the following steps: 1. Set the speed threshold at zero and claim traffic conflicts for a liberally large separation threshold. 2. Estimate the expected number of crashes for gradually decreasing separation thresholds until the crash estimates are stable. 3. If no suitable separation threshold is found in step 2 before running out of conflicts, increase the speed threshold and repeat claiming conflicts with a liberally large separation threshold. 4. Repeat steps 2 and 3 until the lowest speed threshold and the corresponding largest separation threshold are found before running out of conflicts. 5. If no thresholds are found, then the sample is too small or there are other issues. A log-log curves should be inspected. The above procedure was applied to the SHRP2 data and the found threshold speed was 2.5 m/s (5.6 mi/h). Then, the procedure for selecting an appropriate threshold described in Chapter 8 was applied. Fig. 11.6 presents the AIC values obtained for a sequence of tested thresholds. The corresponding separation threshold for male drivers was 1.4 s and for female drivers was 1.5 s. Fig. 11.7 demonstrates the approximate linearity of the log-log functions for the three types of drivers and for the selected threshold separations.
206 Measuring Road Safety with Surrogate Events
FIG. 11.6 Selection of the proper ITTC threshold based on the information-based performance measure AIC (Chapter 7).
Figs. 11.8e11.10 present the standard results for the speed threshold 2.5 m/s (5.6 mi/h) and all the tested separation thresholds. A total of 1,882 events were claimed as conflicts at the initial 2-s separation threshold (measured with ITTC). The filled points in all the graphs indicate unbiased estimates of the expected number of crashes, unbiased estimates of the conditional probability of a crash, and the numbers of correctly claimed traffic conflicts for all three types of driver. The summary of the results is presented in Table 11.2.
Evaluating the results The Lomax estimates of the expected number of rear-end crashes for the three groups of drivers (see Table 11.3) clearly point out young drivers as the most dangerous group and female drivers as the safest group. Not only is the order of the estimates correct but also the magnitude follows well the crash-based estimates. This similarity is particularly encouraging because the conflictbased estimates were obtained from data collected for only 1.4% of trips traveled by the SHRP2 population. To emphasize this benefit, let us make the following comparison. One month of observing conflicts is equivalent to six years of recording crashes. Table 11.3 also presents the 90-percent confidence intervals for the conflict-based crash estimates. The estimated safety difference between young male drivers and mature female drivers is significant. Also considerable seems to be the difference between young and mature male drivers. The safety difference between mature male and mature female drivers is not as significant as in the other pairwise comparisons. Similar conclusions can be made for the crash-based estimates (Table 11.4). The confidence intervals of crash-based
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FIG. 11.7 Log-log curves for the three studied types of drivers.
estimates for the two groups of mature drivers also overlap one another considerably, though to a lower extent than the conflict-based intervals. The estimation efficiency is one of the factors of the results’ conclusiveness. Let the estimation efficiency be measured with the length of the confidence interval (a proxy for dispersion). The dispersion of the conflict-based estimates for young males, mature males, and mature females measured with
208 Measuring Road Safety with Surrogate Events
FIG. 11.8 Male drivers 16e25.
the confidence interval lengths are, respectively, 0.722, 0.191, and 0.062, while for the crash-based estimates they are 0.183, 0.136, and 0.112. The crashbased estimate for young drivers is undoubtedly more confident than the conflict-based counterpart, mainly due to the high crash count. On the other hand, the conflict-based and crash-based estimates for mature males are comparable, as are those for mature females. It seems that traffic conflicts are
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FIG. 11.9 Male drivers 45e64.
particularly beneficial when the frequency of crashes is low. This comparison may be unfair if one forgets to mention that the period of collecting crash data was 70 times longer than the period of observing traffic conflicts. For convenient comparison of the conflict-based estimates with the statistics available for the entire USA population, the crash count estimates have been converted to rates of crashes per 100 million miles traveled. These rates
210 Measuring Road Safety with Surrogate Events
FIG. 11.10 Female drivers 45e64.
are presented in Table 11.5. The similarity of these rates with the rates in Table 11.1 is noticeable.
Summary It may be concluded that the Lomax-based analysis of traffic conflicts for a small portion of the SHRP2 population produced results that are in accordance with general safety knowledge and with the crash-based statistics obtained for the SHRP2 population. The results are encouraging. At best, they allow
Driver type
Miles traveled when car following (sample exposure)
Separation threshold (s)
Traffic conflicts claimed
Parameter k
Conditional crash probability
Expected number of crashes
Males 16 e25
25,142
1.3
75
7.822474
0.004418
0.331331
Males 45 e64
22,596
1.5
71
9.863339
0.001074
0.076225
Females 45e64
37,288
1.5
70
11.90382
0.000261
0.018268
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TABLE 11.2 Summary of results produced with the Lomax-based analysis for threshold speed 2.5 m/s (5.6 mi/h).
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TABLE 11.3 Lomax crash estimates and confidence intervals. Conflict-based for study sample Bootstrap 90% conf. interval Driver type
Lomax mean estimate
Mean
Lower limit
Upper limit
Males 16e25
0.3313
0.3758
0.0936
0.8156
Males 45e64
0.0762
0.0908
0.0206
0.2115
Females 45e64
0.0183
0.0239
0.0033
0.0650
TABLE 11.4 Police-reportable rear-end expected crash estimates. Crashes in all trips (population exposure)
Crashes rescaled to sample exposure
90% conf. interval
90% conf. interval
Driver type
Crash count
Expected count
Lower limit
Upper limit
Expected count
Lower limit
Upper limit
Males 16e25
24
24
16.55
32.59
0.2731
0.1883
0.3709
Males 45e64
6
6
2.61
10.51
0.1030
0.0448
0.1804
Females 45e64
2
2
0.36
4.74
0.0511
0.0092
0.1210
claiming the method’s validity and, at least, they provide evidence that support that the method produced valid results in the analyzed case. It must be stressed that the conflict analysis was simplified by applying convenient instantaneous s values. These values can be readily calculated from the measured quantities instead of predicting them by considering unobserved collision. On the other hand, the frequent traffic interactions at low speeds complicate the analysis. They make hypothetical collisions safe, thus undermining the concept of failure by eliminating the danger even at very short separations. This situation calls for applying a threshold speed above which the presence of risk and the potential of related failure are applicable. Setting the threshold speed should be done with caution to avoid excluding too many legitimate conflicts.
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TABLE 11.5 Estimates of police-reportable rear-end crash rates per 100 million miles of car-following (SHRP2 data). Based on crashes in all trips
Based on traffic conflicts
90% conf. interval Driver type
90% conf. interval
Mean
Lower limit
Upper limit
Bootstrap mean
Lower limit
Upper limit
Males 16 e25
1086
749
1475
1495
372
3244
Males 45 e64
456
198
799
402
91
936
Females 45e64
137
25
325
64
9
174
The attractive advantage of conflict-based analysis is a considerably reduced period of collecting data. In the studied case, it was 70 times. This data collection speed-up depends on the ratio of crashes to conflicts (conditional probability of crash), which may differ from case to case. For example, frequent conflicts with low probability of crash offer the highest speed-up benefit, while infrequent conflicts with high probability of crashes will not. Although the severity of the potential outcome was considered in the context of the presence of hazard and the potential for police-reportable outcome, no attention was put on estimating the severity level of the potential collision outcome. This void can be filled, and it is discussed as a research need in the concluding part of the book.
References Blatt, A., Pierowicz, J.A., Flanigan, M., Lin, P.-S., Kourtellis, A., Lee, C., Hoover, M., 2015. SHRP2 Safety ResearchdNaturalistic Driving Study: Field Data Collection Transportation Research Board at the National Academy of Sciences. Washington, D.C, ISBN 978-0-30927393-0. Retrieved from. http://www.trb.org/Main/Blurbs/170888.aspx. Campbell, K.L., SeptembereOctober 2012. The SHRP 2 naturalistic driving study addressing driver performance and behavior in traffic safety. TR News 282. https://insight.shrp2nds.us/ documents/shrp2_background.pdf. Hankey, J.M., Perez, M.A., McClafferty, J.A., April 2016. Description of the SHRP2 Naturalistic Database and the Crash, Near-Crash, and Baseline Data Sets. Task Report Prepared for the Strategic Highway Research Program 2. Transportation Research Board, The National Academies. Virginia Tech Transportation Institute, Blacksburg, VA.
214 Measuring Road Safety with Surrogate Events Moe`, A., Cadinu, M., Maass, A., 2015. Women drive better if not stereotyped. Accident Analysis and Prevention 85, 199e206. Padilla, J.-L., Doncel, P., Gugliotta, A., Castro, C., October 2018. Which drivers are at risk? Factors that determine the profile of the reoffender driver. Accident Analysis and Prevention 119, 237e247. Saunier, N., Sayed, T., Ismail, K., 2010. Large-scale automated analysis of vehicle interactions and collisions. Transportation Research Record, Journal of the Transportation Research Board 42e50. No. 2147, Transportation Research Board of the National Academies, Washington, D.C. Scott-Parker, B., Watson, B., King, M.J., Hyde, M.K., October 2013. Revisiting the concept of the ‘problem young driver’ within the context of the ‘young driver problem’: who are they? Accident Analysis and Prevention 59, 144e152. Tefft, B.C., November 2012. Motor Vehicle Crashes, Injuries, and Deaths in Relation to Driver Age: United States, 1995e2010 AAA Foundation for Traffic Safety. https://aaafoundation.org/ wp-content/uploads/2018/01/OlderDriverRiskReport.pdf.
Rear-end collisions e naturalistic driving study Chapter outline Data Initial analysis Studied types of drivers Claiming and analyzing traffic conflicts
198 198 202
Evaluating the results Summary References
206 210 213
203
Abstract The data used in this chapter were produced by radar, accelerometer, and speedometer devices installed in SHRP2 vehicles. Considerable data pre-processing was needed. From all the trips made by the studied types of drivers, 1.4% of the trips were randomly selected to search for rear-end conflicts. The detected conflicts were analyzed with the method presented in this book. The crash estimates obtained from these conflicts were converted to rear-end crash rates and compared to the rear-end crash rates calculated for trips made by all the SHRP2 drivers of the three types. The results obtained based on conflicts and crashes compare well. This is an appealing indication of the method’s validity. Another conclusion is that instantaneous times to collision and changes in braking rates constitute sufficient basis to claim rear-end conflicts.
Chapters 9 and 10 presented the Lomax-based analysis of road near-departures and right-angle interactions. This chapter applies the method to rear-end traffic conflicts recorded during naturalistic driving. The primary focus is on demonstrating that the crash frequency estimated with traffic conflicts follows the frequency of actual crashes. The experience gained in the process is shared with the reader to help in successful application of the method to other realworld cases. The data used in this example were collected in a large research programdthe Strategic Highway Research Program 2 (SHRP2) effected between 2006 and 2015 (Blatt et al., 2015). The Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users, passed by the USA congress in 2005, authorized spending $170 million in seven years on the SHRP2, focusing on safety and three other transportation research areas. One of the objectives was to significantly enhance highway safety by improving an Measuring Road Safety with Surrogate Events. https://doi.org/10.1016/B978-0-12-810504-7.00011-2 © 2020 Elsevier Inc. All rights reserved.
197
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understanding of driving behavior through a large-scale study. Campbell reported in 2012 that 23,247 drivers were on the road driving cars as part of their daily routines (Campbell, 2012). At the conclusion of the data collection phase, the database included nearly 5.5 million trips made by 3400 participant drivers. Over 4300 total years of naturalistic driving time between 2010 and 2013 produced and validated 1549 crashes (Hankey et al., 2016). Crashes were defined: “Any contact that the subject vehicle has with an object, either moving or fixed, at any speed in which kinetic energy is measurably transferred or dissipated is considered a crash” (cit. Hankey et al., 2016). Among these crashes, 234 were rear-end collisions including 119 rear-end crashes that happened when SHRP2 drivers followed other vehicles. This chapter applies instantaneous time to collision s to estimate the conditional probability of rear-end crash and the expected number of rear-end crashes in a sample of randomly selected SHRP2 drivers. The results of the analysis are compared to the number of rear-end crashes reported for all SHRP2 drivers during the SHRP2 period. The data and their preparation, analysis, results, and discussion are included.
Data Among various pieces of data collected by instrumented vehicles included in the SHRP2 database, the following data were found useful for claiming traffic conflicts: 1. Radar-measured distance (range) to the lead vehicle reported 10 times per second, 2. Accelerometer-measured longitudinal and lateral acceleration rates of the instrumented vehicle reported 10 times per second, 3. Speedometer-measured speed of the instrumented vehicle reported once every 1e2 s at irregular rates. The speed measurements were assumed accurate based on the information obtained from the Virginia Tech personnel involved in maintaining and processing the SHRP2 data. The gaps between speed measurements were filled with the speed values obtained by integrating the longitudinal acceleration rates. Any discrepancy between the speeds measured with a speedometer and the speeds derived from the acceleration rates were reconciled by adjusting the acceleration-derived speeds through shifting and scaling that minimized the discrepancy between the two measurements. After filling the gaps between the speedometer-measured speeds these speed sequences were smoothed with a moving average of five values.
Initial analysis An initial small sample of 255 trips with traffic conflicts was selected randomly to check and control the data quality and to evaluate and modify
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initially devised methods of traffic conflict detection and analysis. Trips were selected in batches from the population and checked for at least one rear-end traffic conflict with the instantaneous travel time s < 2.0 s. The selection ended when the desired number of trips with at least one traffic conflict were found. The minimum sm value was interpreted as the end of a successful response. Following the concept of generalized separation (Chapter 6), the response delay x was calculated by subtracting sm from the sc threshold: x ¼ sc sm. Fig. 11.1 presents a possible rear-end traffic conflict, which is marked with the oval shape. Time is represented by the number of video frames progressing at the frequency of 10 per second. The evasive braking is represented by the considerable longitudinal jerk, rapidly changing the deceleration rate from -1 m/s2 to -5 m/s2, and with the instantaneous time to collision s falling below 2 s. Following the recommended diagnostic analysis of Chapter 8, the log-log curves log[1 F(x)] ¼ f[log(1 þ x/sc)] calculated with the ordered response delays x were inspected to check for indication of a Lomax distribution of x. A linear relationship with a slope corresponding to parameter ek was expected. The top curve in Fig. 11.2 is the log-log curve obtained for conflicts claimed in the test trips for threshold tc ¼ 2.0 s. The curve is apparently nonlinear. The curve exhibits change in slope at log(1 þ x/sc) ¼ 0.27 and a pronounced upward curve for log(1 þ x/sc) > 0.6. Reducing threshold tc to 1.5 s (middle curve) has moved the first nonlinearity point from 0.27 to 0.07, while the upward curve still appears in a similar location. Although threshold tc set at 1.0 s has eliminated the first nonlinearity point, the upward curve remains
FIG. 11.1 Example rear-end conflict in SHARP2 data marked (inside the oval).
200 Measuring Road Safety with Surrogate Events
FIG. 11.2
Log-log curves for the test sample with the lane exit observations included.
seemingly unchanged (see Fig. 11.2). It is obvious that a long separation threshold is not the cause of the log-log curve non-linearity. Analyzing closely the data with considerable x and short sm revealed a number of rear-end interactions where the s values were not reported at the time of sm or shortly afterward. Video frames with these events revealed lead vehicles changing lanes or leaving the road. Signaling in advance the intended lane change by the lead vehicles and initiating consistent lateral movement allowed the following drivers to anticipate the clearing of the lane. This anticipation prompted the following drivers to continue closing the gap and passing the lead vehicles at short time separations. The numerical data confirmed no or gentle braking while maintaining the unchanged direction by the followers. Some drivers even slightly accelerated before passing the spot where lead vehicles left the lane. These behaviors produced short s values while the drivers kept the situation under control with neither failure nor considerable risk. Such events do not pass the condition of traffic failure and cannot be claimed as conflicts. Fig. 11.3 presents the instrumented vehicles’ speeds at the time of sm values. The cases with a disappearing lead vehicle are represented with the filled circles. Removing these events eliminated the nonlinearity problem. This is demonstrated in Fig. 11.4 with the approximately straight log-log curve for the sc threshold lower than 2.0 s. This result concluded the first phase of the analysis. In the next step, a large sample of 76,389 trips (1.4 % of all SHRP2 trips) was randomly drawn including 12,742 trips with at least one potential traffic conflict (sm <2 s). The data provided for each trip included information about the trips, drivers, and vehicles. Additional 40-second video clips were requested for periods with questionable radar, speedometer, and accelerometer data.
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2.0 1.8 1.6
Wm value (s)
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0
10
20
30 40 Speed at Wm (mi/h)
Lane Exiting
50
60
70
80
Remaining in Lane and Braking
FIG. 11.3 Minimum instantaneous time to collision observations in the test sample.
The exposure for the entire population of drivers is relevant in the scope of the study. Hence, the total number of miles driven by all the SHRP2 drivers was obtained. In addition, the crash data information was acquired for validation of the number of crashes predicted using conflicts. The safety analysis proceeded with additional quality control. The speeds of the lead vehicles were estimated by subtracting speeds of the following vehicles from the respective range rates measured with the radar. The derived new quantity helped detect cases of lead vehicles supposedly moving in the reverse direction toward the instrumented vehicles. The negative but small radar measurements between -1 m/s and 0 m/s were assumed unreliable and
FIG. 11.4 Log-log curves for the test sample after removing the lane exit observations (sc ¼ 2.0 s).
202 Measuring Road Safety with Surrogate Events
ignored. There was also a considerable number short-lived “backward motions” associated with sudden reductions in s and small sm. Inspecting the relevant video images revealed that indeed a limited number vehicles were in the field of view of radar when moving in the opposite direction on the other side of the road. In the majority of cases though, vehicles were entering gaps in front of the instrumented vehicles. During the entering maneuver, a side of the entering vehicles were exposed to the radar beams. The beams were sliding along the sides of the gap-entering vehicles backward creating an illusion of backward movement. The entering vehicles were inheriting the ID of the other vehicles in front. This continuity of ID was increasing the appearance of legitimacy of the incorrect measurements. All the cases with negative speeds of lead vehicles were excluded from the analysis. Values of sm smaller than 0.1 s, including zero, were associated with low and positive speeds and short ranges often followed by periods with missing radar readings. The first hypothesis was made that these events were safe collisionsdphysical contacts between vehicles with neither bodily injury nor reportable material damage. According to the SHRP2 definition of crash, these events should not be defined as crashes. The Virginia Tech SHRP2 team checked several identified cases to confirm that these indeed were not collisions. A plausible explanation for missing radar readings was that low relative speeds and short ranges made the radar unreliable, and this might lead to inaccurate or missing readings. The quality control phase reduced the 18,453 potential conflicts to 7,424. The data processing moved to the final phase of claiming traffic conflicts that involved drivers of studied categories, and concurrent estimation and inspection of the expected number of crashes, and log-log curves to ensure the correctness of the results. This analysis was applied to data obtained for three types of studied drivers.
Studied types of drivers Past studies indicated that young drivers were strongly overrepresented in road crashes (Scott-Parker et al., 2013). Young drivers are frequently pointed out by police officers preparing crash reports as those who caused the crashes or contributed to their occurrence. Safety experts associate the proneness of young drivers to crashes with their limited driving experience and consequently substandard driving skills. Fig. 11.4 compares crash rates by drivers of various ages. These rates account for the exposure measured with miles traveled. The predominance of young drivers age 16e25 in crash involvement is undeniable. On the other hand, the most safe drivers are of age 40e69 who are experienced and enjoy relatively good physical and mental performance. Other research studies consistently point out that female drivers tend to drive more safely than males (Moe` et al., 2015) and are involved in fewer crashes than male drivers (Padilla et al., 2018).
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The past research studies clearly indicate that among the three groups of drivers, (1) young male 16e25, (2) mature male 46e65, and (3) mature female 46e65, young males are the worst drivers while the mature females are the best. The difference between the driving performance of young males and of mature drivers is much bigger than between mature male and female drivers. Table 11.1 presents statistics of the rear-end crashes caused by the three types of drivers during the SHRP2 program. The subject drivers were in the SHRP2 instrumented vehicles and following other vehicles when colliding with the vehicles in front of them (front hit). The numbers are generally consistent with the current knowledge on the subject and specifically with the crash rates in Fig. 11.5. It should be stressed that the rear-end crash involvement rate in Fig. 11.5 includes front hits and back hits of vehicles driven by drivers in the age groups.
Claiming and analyzing traffic conflicts An important question remaining to be answered is if the proposed Lomaxbased method is able to produce rear-end crash rate estimates that are similar to the values listed in Table 11.1. To answer this question, the Lomaxbased method was applied to traffic conflicts that occurred in a small portion of the 1.4 % trips randomly selected from all the trips made during the SHRP2 program by drivers of the types listed in Table 11.1. The events with minimum ITTC values immediately followed by lane departures of lead vehicles were eliminated. Also, all events with negative speeds of lead vehicles were removed as most likely caused by entering the gaps between lead and instrumented vehicles.
TABLE 11.1 Rear-end crash counts and rates during the SHRP2 study period (SHRP2 population). Miles driven while following another vehicle (SHRP2 population exposure)
Number of rear-end crashes (front hits)
Males 16e25
2,209,414
Males 45e64 Females 45e64
Driver type
Police reportable rear-end crashes (front hits)
Count
Rate per 100 million miles of car following
31
24
1086
1,316,178
10
6
456
1,460,122
2
2
137
204 Measuring Road Safety with Surrogate Events
FIG. 11.5
Involvement of various age groups of drivers in crashes (Tefft, 2012).
Besides the central question of failure-caused small separations between road users is the inevitability of collision if no evasion action is undertaken and successfully completed. One possible approach proposed and elaborated by Saunier et al. (2010) is predicting probable movements as continuation of conflict-free behavior that mimics the lack of hazard awareness. The prediction confirms in a counterfactual way the crash potential and provides estimates of the time to collision. Another method applied here is confirming that the observed behavior indicates the presence of collision avoidance, and using the instantaneous time to collision to approximate the time to hypothetical collision. Detecting an evasive action of a driver following another car is a confirmation that the conflict was resolved most likely by the follower and was not a coincidental acceleration of the preceding car. Two conditions were used to detect evasion: (1) there is a statistically detectable (significant) jerk in the motion of the follower immediately before the shortest instantaneous time to collision sm that (2) leads to a considerable braking at a rate of at least 1.5 m/ s2. These conditions were later confirmed as producing, with other conditions, the expected trend in the results: stable estimation of the expected number of crashes for a sequence of separation thresholds. Another matter that needed attention was that of low speeds in the period preceding a potential traffic conflict. Claiming traffic conflicts even for short separations but under low speeds may produce false positives. The source of the estimation problem is two-fold. (1) Drivers moving at low speeds may perceive no considerable risk. One would rightly claim that this is consistent with no real hazard because a small relative speed at impact produces harm neither to vehicles nor to vehicle occupants. Consequently, it is difficult to claim that a safety-related failure is possible when there is no hazard. (2) Even if an impact speed is sufficiently high to expect some damage, the outcome may still be too minor to be police-reportable. The latter concern is less critical than the former concern because it can be rectified in the subsequent analysis
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by applying a discrete-outcome model to estimate the probability of policereportable outcome. Mostly due to the concern of no hazard perception among involved drivers, traffic interactions at too low speeds should be ignored to avoid falsely claimed conflicts. Speed should be sufficiently high at collision to induce a fear of collision among participating drivers. Determining the suitable threshold for impact speed above which a conflict may be claimed is similar to determining a threshold for separation. Specifically, the threshold speed can be determined as the lowest speed at which estimates of the expected crash frequency for different separation thresholds is stable. There is an important note to make. While a low separation threshold does not introduce any bias to the crash frequency estimates, a too high speed threshold leads to underestimation of the number of crashes by neglecting valid conflicts associated with potentially serious outcomes. The speed at the hypothetical collision to be considered in the expanded procedure can be estimated with the following equation: d Impact speedðtm þ sm Þ ¼ Range rateðtm Þ þ sm $ Range rateðtm Þ dt
(11.1)
where tm is the time at which s reaches the minimum value sm. Time t ¼ tm þ sm is the approximate moment when the hypothetical collision happens if sm is short and close to time to collision T. The expanded procedure applied in the presented SHRP2 study includes the following steps: 1. Set the speed threshold at zero and claim traffic conflicts for a liberally large separation threshold. 2. Estimate the expected number of crashes for gradually decreasing separation thresholds until the crash estimates are stable. 3. If no suitable separation threshold is found in step 2 before running out of conflicts, increase the speed threshold and repeat claiming conflicts with a liberally large separation threshold. 4. Repeat steps 2 and 3 until the lowest speed threshold and the corresponding largest separation threshold are found before running out of conflicts. 5. If no thresholds are found, then the sample is too small or there are other issues. A log-log curves should be inspected. The above procedure was applied to the SHRP2 data and the found threshold speed was 2.5 m/s (5.6 mi/h). Then, the procedure for selecting an appropriate threshold described in Chapter 8 was applied. Fig. 11.6 presents the AIC values obtained for a sequence of tested thresholds. The corresponding separation threshold for male drivers was 1.4 s and for female drivers was 1.5 s. Fig. 11.7 demonstrates the approximate linearity of the log-log functions for the three types of drivers and for the selected threshold separations.
206 Measuring Road Safety with Surrogate Events
FIG. 11.6 Selection of the proper ITTC threshold based on the information-based performance measure AIC (Chapter 7).
Figs. 11.8e11.10 present the standard results for the speed threshold 2.5 m/s (5.6 mi/h) and all the tested separation thresholds. A total of 1,882 events were claimed as conflicts at the initial 2-s separation threshold (measured with ITTC). The filled points in all the graphs indicate unbiased estimates of the expected number of crashes, unbiased estimates of the conditional probability of a crash, and the numbers of correctly claimed traffic conflicts for all three types of driver. The summary of the results is presented in Table 11.2.
Evaluating the results The Lomax estimates of the expected number of rear-end crashes for the three groups of drivers (see Table 11.3) clearly point out young drivers as the most dangerous group and female drivers as the safest group. Not only is the order of the estimates correct but also the magnitude follows well the crash-based estimates. This similarity is particularly encouraging because the conflictbased estimates were obtained from data collected for only 1.4% of trips traveled by the SHRP2 population. To emphasize this benefit, let us make the following comparison. One month of observing conflicts is equivalent to six years of recording crashes. Table 11.3 also presents the 90-percent confidence intervals for the conflict-based crash estimates. The estimated safety difference between young male drivers and mature female drivers is significant. Also considerable seems to be the difference between young and mature male drivers. The safety difference between mature male and mature female drivers is not as significant as in the other pairwise comparisons. Similar conclusions can be made for the crash-based estimates (Table 11.4). The confidence intervals of crash-based
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FIG. 11.7 Log-log curves for the three studied types of drivers.
estimates for the two groups of mature drivers also overlap one another considerably, though to a lower extent than the conflict-based intervals. The estimation efficiency is one of the factors of the results’ conclusiveness. Let the estimation efficiency be measured with the length of the confidence interval (a proxy for dispersion). The dispersion of the conflict-based estimates for young males, mature males, and mature females measured with
208 Measuring Road Safety with Surrogate Events
FIG. 11.8 Male drivers 16e25.
the confidence interval lengths are, respectively, 0.722, 0.191, and 0.062, while for the crash-based estimates they are 0.183, 0.136, and 0.112. The crashbased estimate for young drivers is undoubtedly more confident than the conflict-based counterpart, mainly due to the high crash count. On the other hand, the conflict-based and crash-based estimates for mature males are comparable, as are those for mature females. It seems that traffic conflicts are
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209
FIG. 11.9 Male drivers 45e64.
particularly beneficial when the frequency of crashes is low. This comparison may be unfair if one forgets to mention that the period of collecting crash data was 70 times longer than the period of observing traffic conflicts. For convenient comparison of the conflict-based estimates with the statistics available for the entire USA population, the crash count estimates have been converted to rates of crashes per 100 million miles traveled. These rates
210 Measuring Road Safety with Surrogate Events
FIG. 11.10 Female drivers 45e64.
are presented in Table 11.5. The similarity of these rates with the rates in Table 11.1 is noticeable.
Summary It may be concluded that the Lomax-based analysis of traffic conflicts for a small portion of the SHRP2 population produced results that are in accordance with general safety knowledge and with the crash-based statistics obtained for the SHRP2 population. The results are encouraging. At best, they allow
Driver type
Miles traveled when car following (sample exposure)
Separation threshold (s)
Traffic conflicts claimed
Parameter k
Conditional crash probability
Expected number of crashes
Males 16 e25
25,142
1.3
75
7.822474
0.004418
0.331331
Males 45 e64
22,596
1.5
71
9.863339
0.001074
0.076225
Females 45e64
37,288
1.5
70
11.90382
0.000261
0.018268
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TABLE 11.2 Summary of results produced with the Lomax-based analysis for threshold speed 2.5 m/s (5.6 mi/h).
211
212 Measuring Road Safety with Surrogate Events
TABLE 11.3 Lomax crash estimates and confidence intervals. Conflict-based for study sample Bootstrap 90% conf. interval Driver type
Lomax mean estimate
Mean
Lower limit
Upper limit
Males 16e25
0.3313
0.3758
0.0936
0.8156
Males 45e64
0.0762
0.0908
0.0206
0.2115
Females 45e64
0.0183
0.0239
0.0033
0.0650
TABLE 11.4 Police-reportable rear-end expected crash estimates. Crashes in all trips (population exposure)
Crashes rescaled to sample exposure
90% conf. interval
90% conf. interval
Driver type
Crash count
Expected count
Lower limit
Upper limit
Expected count
Lower limit
Upper limit
Males 16e25
24
24
16.55
32.59
0.2731
0.1883
0.3709
Males 45e64
6
6
2.61
10.51
0.1030
0.0448
0.1804
Females 45e64
2
2
0.36
4.74
0.0511
0.0092
0.1210
claiming the method’s validity and, at least, they provide evidence that support that the method produced valid results in the analyzed case. It must be stressed that the conflict analysis was simplified by applying convenient instantaneous s values. These values can be readily calculated from the measured quantities instead of predicting them by considering unobserved collision. On the other hand, the frequent traffic interactions at low speeds complicate the analysis. They make hypothetical collisions safe, thus undermining the concept of failure by eliminating the danger even at very short separations. This situation calls for applying a threshold speed above which the presence of risk and the potential of related failure are applicable. Setting the threshold speed should be done with caution to avoid excluding too many legitimate conflicts.
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TABLE 11.5 Estimates of police-reportable rear-end crash rates per 100 million miles of car-following (SHRP2 data). Based on crashes in all trips
Based on traffic conflicts
90% conf. interval Driver type
90% conf. interval
Mean
Lower limit
Upper limit
Bootstrap mean
Lower limit
Upper limit
Males 16 e25
1086
749
1475
1495
372
3244
Males 45 e64
456
198
799
402
91
936
Females 45e64
137
25
325
64
9
174
The attractive advantage of conflict-based analysis is a considerably reduced period of collecting data. In the studied case, it was 70 times. This data collection speed-up depends on the ratio of crashes to conflicts (conditional probability of crash), which may differ from case to case. For example, frequent conflicts with low probability of crash offer the highest speed-up benefit, while infrequent conflicts with high probability of crashes will not. Although the severity of the potential outcome was considered in the context of the presence of hazard and the potential for police-reportable outcome, no attention was put on estimating the severity level of the potential collision outcome. This void can be filled, and it is discussed as a research need in the concluding part of the book.
References Blatt, A., Pierowicz, J.A., Flanigan, M., Lin, P.-S., Kourtellis, A., Lee, C., Hoover, M., 2015. SHRP2 Safety ResearchdNaturalistic Driving Study: Field Data Collection Transportation Research Board at the National Academy of Sciences. Washington, D.C, ISBN 978-0-30927393-0. Retrieved from. http://www.trb.org/Main/Blurbs/170888.aspx. Campbell, K.L., SeptembereOctober 2012. The SHRP 2 naturalistic driving study addressing driver performance and behavior in traffic safety. TR News 282. https://insight.shrp2nds.us/ documents/shrp2_background.pdf. Hankey, J.M., Perez, M.A., McClafferty, J.A., April 2016. Description of the SHRP2 Naturalistic Database and the Crash, Near-Crash, and Baseline Data Sets. Task Report Prepared for the Strategic Highway Research Program 2. Transportation Research Board, The National Academies. Virginia Tech Transportation Institute, Blacksburg, VA.
214 Measuring Road Safety with Surrogate Events Moe`, A., Cadinu, M., Maass, A., 2015. Women drive better if not stereotyped. Accident Analysis and Prevention 85, 199e206. Padilla, J.-L., Doncel, P., Gugliotta, A., Castro, C., October 2018. Which drivers are at risk? Factors that determine the profile of the reoffender driver. Accident Analysis and Prevention 119, 237e247. Saunier, N., Sayed, T., Ismail, K., 2010. Large-scale automated analysis of vehicle interactions and collisions. Transportation Research Record, Journal of the Transportation Research Board 42e50. No. 2147, Transportation Research Board of the National Academies, Washington, D.C. Scott-Parker, B., Watson, B., King, M.J., Hyde, M.K., October 2013. Revisiting the concept of the ‘problem young driver’ within the context of the ‘young driver problem’: who are they? Accident Analysis and Prevention 59, 144e152. Tefft, B.C., November 2012. Motor Vehicle Crashes, Injuries, and Deaths in Relation to Driver Age: United States, 1995e2010 AAA Foundation for Traffic Safety. https://aaafoundation.org/ wp-content/uploads/2018/01/OlderDriverRiskReport.pdf.