Development of Analysis Methods Using Recent Data (2012)

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4Background and Project Objectives C h a p t e r 1 Background In its essence, rational planning involves using predicted con- sequences to guide selection from among a set of possible actions. In road safety engineering, this requires being able to predict the frequency and severity of crashes that are expected to result from a given design or operational configuration. Hauer (1) has argued persuasively for developing a scientifi- cally justifiable methodology for making these predictions, and the last 10 years have seen two major initiatives in the United States related to this issue. One is the development of the Highway Safety Manual (HSM), the first edition of which was released in 2010 by the American Association of State Highway and Transportation Officials (AASHTO). The other is the safety focus of the SHRP 2 research program. highway Safety Manual The goal of the HSM is to provide highway professionals with tools for explicitly considering the safety impacts of engineer- ing actions. The dominant methodology used to develop the HSM is statistical analysis of crash-frequency data, where the basic units of analysis are either sections of highway or inter- sections and where the dependent variables are crash frequen- cies observed over one or more years. In some cases, these frequencies can be broken down by crash type or severity. Gen- eralized linear models are used to describe baseline associa- tions between crash frequency and observable road features, while the effects of changes from these baseline conditions are captured through empirically determined crash-modification factors. The effect of an intervention is then predicted by first using the base model to predict crash frequency under the pre- vailing conditions, and then multiplying this expected fre- quency by a crash-modification factor that reflects the effect of the change of interest. Ideally, the crash-modification factor was estimated from a well-conducted before/after study that controlled for selection bias effects. The strong reliance of the HSM ’s first edition on this type of statistical modeling is in large part the result of historical developments, where the inte- grated crash and roadway databases maintained by the High- way Safety Information System (HSIS) and several individual states had attained a useful degree of completeness and the development of empirical Bayes and hierarchical Bayes meth- ods during the 1980s and 1990s brought the supporting statis- tical tools to a useful degree of maturity. Regression analyses of aggregated observational data have well-understood limits to their ability to discover and describe underlying causal processes (2). In 2006, a daylong workshop was held during the annual meeting of the Transportation Research Board (TRB), which focused on elucidating these limits and discussing alternative methods. At that workshop, Bonneson and Lord (3) pointed out an interesting analogy with the development of the Highway Capacity Manual, where first-generation regression models for predicting traffic signal delay using naïve specifications of independent variables were later replaced by regression models where the form of the independent variables was justified theoretically. These in turn were replaced by models where the functional forms relating traffic flow, capacity, and signal timing to delay were justified theoretically. The macroscopic methods developed for the Highway Capacity Manual were later supplemented and in some instances replaced by microscopic traffic simula- tion models. Hope was expressed that a similar evolution might occur for the HSM, with first-edition regression models being supplemented or replaced by structural models that explicitly describe the mechanisms’ underlying crash occur- rence. A better understanding of crash mechanisms could also support the use of microscopic traffic simulation models to predict the safety consequences of engineering decisions, sim- ilar to how microscopic models are now used to predict oper- ational consequences. As researchers working in this area are acutely aware, however, a major obstacle to progress is the lack of good microscopic data regarding crash occurrence and driver behavior more generally.

5crash-related events. The focus of the present project is on crashes involving more than one vehicle, resulting from car- following or gap-selection behavior of the types often occur- ring at intersections. Structural Modeling of Crash-related events The starting point is Pearl’s (5) notion of a causal model, which in the abstract consists of a set of exogenous variables, a set of endogenous variables, and, for each endogenous variable, a structural equation describing how the variable responds to changes in other model variables. A causal model can be represented qualitatively using a directed graph, with the nodes of the graph representing variables and directed arrows indicating direct causal dependencies. Figure 1.1 displays a simple graphical model for a generic crash. The node u, possibly vector-valued, denotes variables describing background conditions. The node x denotes the variable describing an evasive action, and the node y denotes the crash condition. The crash condition y is assumed to be a deterministic function of u and x, such that y(u,x) = 0, if the values for u and x do not produce a crash y(u,x) = 1, if u and x produce a crash To make these ideas more concrete, consider a simple two- vehicle, rear-ending collision model (6, 7). Such an event might be observed in the field, or it could arise within a microscopic traffic simulation. The initial speed and braking deceleration of the leading vehicle are denoted by v1 and a1, respectively; the initial speed and braking deceleration of the following vehicle by v2 and a2, respectively; and the following driver’s headway and reaction time by h2 and r2, respectively. A collision occurs when the stopping distance available to the following driver is less than that needed to stop without col- liding with the lead vehicle. Using simple physics, this can be expressed as v r v a h v v a2 2 2 2 2 2 2 1 2 12 2 1 1− > − ( . ) If the following driver’s deceleration is taken as the avoid- ance action, then for the rear-end collision, the variables Shrp 2 Safety program As originally conceived, the safety focus area of the SHRP 2 research program comprised two major field studies: a vehicle- based study involving “volunteer drivers and a sophisticated instrumentation package installed in the volunteers’ vehicles” and a site-based study involving video recording of vehicle movements at specific locations. These studies were “intended to support a comprehensive safety assessment of how driver behavior and performance interact with roadway, environ- mental, vehicular, and human factors and the influence of these factors and their interactions on collision risk” (4). At present, the vehicle-based study is going forward while the site-based study has been limited to preliminary design, with further work dependent on the availability of additional funding. The SHRP 2 S01 projects develop and apply analytic methods relevant to these field studies by identifying salient research questions and then attempting to answer them using existing data of the type expected from the field studies. The S01 request for proposal explicitly identified as important “application of crash surrogates” and “the formulation of analytic methods to quantify the relationship of human fac- tors, driver behavior, vehicle, roadway, and environmental factors to collision risk.” Special attention was directed to roadway departure and inter section crashes. There is little doubt that the SHRP 2 vehicle-based study should produce a rich and unprecedented source of infor- mation concerning driver behavior in normal and crash situations and that this should support development and evaluation of vehicle-based safety technologies. The study should also support traditional statistical investigations seek- ing to identify associations between roadway conditions and crash occurrence. In the project team’s view, the SHRP 2 field studies could also provide data supporting the develop- ment and application of microscopic crash models, similar to how existing crash record and roadway databases support the development and application of regression-based approaches. For this to occur, however, analytic tools are needed that can fit and test microscopic models using field study data and can extract the sort of measurements needed to quantify driver behavior in crash-related conditions. The S01 project thus has two interrelated objectives. The first is to develop analytic tools and demonstrate how these can be used to conduct structural model development, using the sort of data expected from the SHRP 2 field studies. The second is to develop a rigorous method for characterizing near crashes so that observations of near crashes might serve as useful surrogates for actual crashes. The approach taken by the project team can be called trajectory-based reconstruction of crash-related events. That is, time history data of vehicle positions, speeds, or both are used to estimate values for variables describing drivers’ actions and characterizing the conditions leading to u x y Figure 1.1. Graphical model of a crash-related event.

6where yk(t) denotes the (one-dimensional) position of Vehi- cle k at time t, vk denotes the initial speed of Driver k, ak denotes his or her braking acceleration, and t0k denotes the time at which braking began. This model can be connected to the rear-end collision model described by noting that the reaction time of Driver k is simply r t tk k k= − −0 0 1 41 ( . ) while the initial following headway between Vehicles k and k-1 when Driver k-1 began braking is h y t y t vk k k k k k= ( ) − ( )( )− − −0 0 1 51 1 1 ( . ) At least for simple event types like this, it is then possible to generate estimates of initial speeds, braking rates, and times of braking initiation by fitting Equation 1.3 to observed trajectories. Davis and Swenson (7) describe how Bayes esti- mates could be computed from trajectory data of the type displayed in Figure 1.2. Table 1.1 summarizes the resulting estimates for these data. In principle, then, trajectory-based reconstruction can be used to fit structural models and estimate important features of crash-related events. One of the project team’s objectives is to extend these methods to handle more complicated situa- tions and to exploit the type of data expected from the SHRP 2 in-vehicle field study. Crash Surrogates The second objective of this project is to develop a quantitative method for characterizing and identifying events that can serve as useful crash surrogates. This is because crashes, especially severe crashes, tend to be rare, so that if one could identify near crashes or other surrogate events that carry information about (v1, a1, v2, r2, h2) are components of u, a2 is the evasive action, and the collision function is y u x if v r v a h v v a if v r , , , ( ) = − ≤ −0 2 2 1 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 1 2 12 2 1 2 − > − v a h v v a ( . ) In this treatment, an event consists of a specification of values for each of the model variables. This specification, plus Structural Equation 1.2, is sufficient to determine whether that event leads to a crash. As they are currently implemented, microscopic simulation models are restricted to combina- tions of values that do not lead to crashes, and an open research question involves determining realistic relative fre- quencies for those combinations that do. To help illustrate the usefulness of this approach, an exam- ple originally presented by Davis and Swenson (7) is used. Fig- ure 1.2 shows trajectories for a platoon of seven vehicles successively braking to stops while traveling in the same lane of a freeway. The leftmost vehicle was the first vehicle in the pla- toon, the rightmost vehicle was the last, and a collision occurred between the two rightmost vehicles. These trajectories were constructed from a video recording of the event by first digitiz- ing each vehicle’s position on successive video frames and then using standard photogrammetry methods to convert from image coordinates to ground coordinates. Applying the simple braking model described, each of these trajectories can be described by the physical model , 0 0 0 2, 0 0 (1.3) 0 2 , 0 2 2 ) ) ) ( ( ( )( ≤ = + − < ≤ + − − > + − v t t t y t v t a t t t t t v a v t v a t t v a k k k k k k k k k k k k k k k k k k -100 -50 0 50 100 150 200 20 30 40 50 60 Time in sec Location feet Vehicle 1 Vehicle 2 Vehicle 3 Vehicle 4 Vehicle 5 Vehicle 6 Vehicle 7 Figure 1.2. Trajectories of seven vehicles braking successively to stops.

7any combination of control inputs that approaches the limit of the vehicle capabilities” (9). Both these definitions assume a counterfactual definition of the surrogate event, where a crash would have occurred had an evasive action not been performed. The 100-car study definition places an additional condition, however, that the magnitude of the evasive action should be in some sense extreme. To see the value of this additional condition, it is helpful to return to Table 1.1. The table gives estimates of initial speeds, headways, reaction times, and the actual and minimum successful decelerations estimated from the vehi- cle trajectories. First, consider the interaction between Vehi- cles 1 and 2. The minimum deceleration by Vehicle 2 needed to avoid collision was about -6.2 ft/s2, while the actual decel- eration was about -6.5 ft/s2. Had the deceleration been slightly less, other things being equal, a crash would have occurred. So, arguably, this event satisfies the ICSTCT defini- tion of a conflict. Most would agree, though, that it does not satisfy the 100-car study condition that the evasive action be extreme. For the interaction between Vehicles 5 and 6, the minimum successful deceleration was about -17.1 ft/s2 and the actual deceleration was about -17.3 ft/s2. This event also satisfies the ICSTCT definition of conflict but comes closer to satisfying the 100-car study condition as well. The project team uses causal models to construct a quantitative measure that captures this difference. To start, Figure 1.3 shows the probability of collision as a function of the following vehicle’s braking deceleration for both vehicle pairs. The analysis is probabilistic because the values of the important event variables are not known with certainty but rather only up to their posterior distributions given the trajectory data. Figure 1.3 was prepared by setting the follower’s deceleration to each of a set of target values and then using Monte Carlo simulation to compute the probabil- ity of a crash. Figure 1.3 shows that for Vehicles 1 and 2, decelerations greater than about -7 ft/s2 prevent a crash with high proba- bility, while for Vehicles 5 and 6, decelerations greater than about -20 ft/s2 are needed for a similar degree of certainty. The latter seems qualitatively close to the definition of near crash used in the 100-car study, but to quantify this degree of closeness, it is necessary to specify what is meant by an eva- sive action that approaches the limit of the vehicle’s capabili- ties. One, but not necessarily the only, way to do this is to apply the results of the emergency braking study carried out by Fambro et al. (10), where the distribution of braking decelerations used by drivers confronted with a surprise braking situation had a mean of about -20.3 ft/s2 and a stan- dard deviation of about 2.6 ft/s2. Figure 1.4 adds to Figure 1.3 a normal distribution with the given mean and standard deviation. Roughly speaking, the degree to which a conflict qualifies as a near crash is how crashes occur, the value of both in-vehicle and site-based studies would increase. Roughly speaking there are two ways that near-crash events might be used as crash surrogates. On the one hand, one might carry out an intensive study of how individual near crashes occurred, with the goal of identifying causal factors for each event. This would be similar to using investigation and reconstruction of actual crashes to gain insight into how and why crashes occur. On the other hand, one might use counts of near crashes as a dependent variable and then look to see how these are associated with roadway or driver char- acteristics. This would be similar to carrying out a statistical study of crash frequency. In either case, though, the starting point is a set of noncrash events and the need to determine the extent to which each could be regarded as a near crash. Returning to the literature, it is possible to find two related but different approaches to defining crash surrogates. One is the definition of conflict as put forward by the International Calibration Study of Traffic Conflict Techniques (ICSTCT): “A traffic conflict is an observable situation in which two or more road users approach each other in space and time to such an extent that there is a risk of collision if their move- ments remain unchanged” (8). However, it turned out that when attempting to find empirical associations between con- flict and crash frequencies, it was helpful if conflicts could be graded as to their seriousness or severity. This distinction is included in the definition of near crash used in the 100-car study, which can be regarded as a pilot for the SHRP 2 vehicle- based field study: “Any circumstance that requires a rapid, evasive maneuver by the subject vehicle, or any other vehicle, pedestrian, cyclist, or animal to avoid a crash. A rapid, evasive maneuver is defined as a steering, braking, accelerating, or Table 1.1. Estimates of Speed, Headway, Reaction Time, Braking Deceleration, and Minimal Successful Deceleration for Seven Vehicles Vehicle (k)a vk (ft/s)b hk (s)c rk (s)d ak (ft/s2)e ako (ft/s2)f 1 50.0 — —   -6.8 — 2 46.7 1.69 1.91   -6.5   -6.2 3 41.8 2.00 4.21 -12.6 -11.4 4 42.3 1.87 1.86 -14.2 -12.8 5 39.3 1.21 1.44 -16.0 -14.4 6 42.3 1.17 1.07 -17.3 -17.1 7 41.7 1.24 1.65 -20.3 -24.8 a Number of vehicles b Speed of the k vehicle c Headway of the k vehicle d Reaction time of the k vehicle e Braking acceleration f Minimum deceleration needed to avoid collision

8tions, are treated as inputs to a physical model describing vehicle motion. The team’s choice of this modeling strategy is rooted in the fact that models of this sort are needed if realistic crash processes are to be included in microscopic traffic simulation models. The team has illustrated how a simple version of a trajectory model can be used to estimate features of crash and near-crash events, such as driver reac- tion times, following headways, and deceleration rates, from trajectory data of the sort produced from a site-based field study. Given sufficiently large samples of crash and near- crash events, this method could be used to compile distribu- tions for these inputs, which could, in turn, be used in traffic simulation models. Finally, the team has also illustrated how a trajectory model, together with estimates of input variables, can quantify the degree to which a noncrash event could have been a crash. One potential application of this technique would be to process a set of noncrash events produced either determined by how much of this extreme braking distribu- tion lies to the left of the crash probability curve. More for- mally, the probability that a conflict could have been a crash is found by integrating the crash probability curve with respect to the extreme braking distribution. Although analytically intractable, this computation is readily carried out using Monte Carlo methods. Table 1.2 gives these results for each of the noncolliding vehicle pairs from Table 1.1, and the sum of these probabilities can be taken as the expected number of crashes in this set of conflict events had the evading drivers taken their decelerations from the given distribution. Summary To summarize, the project team has introduced an approach to microscopic modeling of crash-related events, where driver actions, together with initial speeds and vehicle loca- 0 0.2 0.4 0.6 0.8 1 1.2 10 0 5 15 20 25 30 Probability of crash Vehicles 1 & 2 Vehicles 5 & 6 Deceleration (feet/sec2) Note: x axis shows decelerations as positive quantities. Figure 1.3. Crash probability as a function of counterfactual values for following vehicle’s deceleration. Vehicles 1 & 2 Vehicles 5 & 6 Evasive probability distribution 10 0 5 15 20 25 0 0.2 0.4 0.6 0.8 1 1.2 Probability of crash Deceleration (feet/sec2) Note: x axis shows decelerations as positive quantities. Figure 1.4. Crash probability versus following vehicle deceleration and probability density function for emergency decelerations.

9references 1. Hauer, E. The Engineering of Safety and the Safety of Engineering. In Challenging the Old Order: Towards New Directions in Traffic Safety Theory (J. Rothe, ed.), Transaction Publishers, London, 1990, pp. 29–71. 2. Freedman, D. From Association to Causation via Regression. In Causality in Crisis? (V. McKim and S. Turner, eds.), University of Notre Dame Press, Notre Dame, Ind., 1997, pp. 113–162. 3. Bonneson, J., and D. Lord. Theory, Explanation, and Prediction in Road Safety. Presented at 85th Annual Meeting of the Transporta- tion Research Board, Washington, D.C., 2006. 4. SHRP 2 Request for Proposals: Development of Analysis Methods Using Recent Data. Transportation Research Board of the National Academies, Washington, D.C., September 11, 2006. 5. Pearl, J. Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge, United Kingdom, 2000. 6. Brill, E. A Car-Following Model Relating Reaction Times and Tem- poral Headways to Accident Frequency. Transportation Science, Vol. 6, No. 4, 1972, pp. 343–353. 7. Davis, G., and T. Swenson. Collective Responsibility for Freeway Rear-Ending Accidents? An Application of Probabilistic Causal Models. Accident Analysis and Prevention, Vol. 38, 2006, pp. 728–736. 8. Guttinger, V. Conflict Observation in Theory and Practice. In Inter­ national Calibration Study of Traffic Conflict Techniques (E. Asmussen, ed.), Springer-Verlag, Berlin, 1984, pp. 17–24. 9. Dingus, T., S. Klauer, V. Neale, A. Petersen, S. Lee, J. Sudweeks, M. Perez, J. Hankey, D. Ramsey, S. Gupta, C. Bucher, Z. Doerzaph, J. Jermeland, and R. Knipling. The 100­Car Naturalistic Driving Study: Phase II—Results of the 100­Car Field Experiment. Report DOT HS 810 593. National Highway Traffic Safety Administration, U.S. Department of Transportation, 2006. 10. Fambro, D., K. Fitzpatrick, and R. Koppa. NCHRP Report 400: Determination of Stopping Sight Distances. Transportation Research Board, National Research Council, Washington, D.C., 1997. by a single driver or at a single location to produce an expected number of crashes in this set. This expected number of crashes could then serve as a dependent variable in a study of driver or site features believed to be related to safety. The remainder of this report describes the effort to extend these ideas to more complicated scenarios using data pro- duced by both vehicle-based and site-based field studies. Chapter 2 outlines the analytic procedures and tools devel- oped for this project and illustrates their use. Chapter 3 pre- sents analyses of data obtained from the 100-car vehicle-based field study. Chapter 4 describes analyses of data from site- based video on Interstate 94, while Chapter 5 describes work with site-based radar data from the Cooperative Intersection Collision Avoidance Systems (CICAS) intersection in North Carolina. Chapter 6 presents the study’s conclusions and recommendations. Table 1.2. Crash Probabilities for Each Vehicle Pair, Obtained Using the Emergency Braking Distribution Lead Vehicle Following Vehicle P (crash)a 1 2 0 2 3 0 3 4 0 4 5 .004 5 6 .138 Sum .142 a Probability of crash