A Multivariate Analysis of Crash and Naturalistic Driving Data in Relation to Highway Factors (2013)

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12 Surrogates for Road Departure Crashes Overview of Available Surrogates In Chapter 5, the statistical analysis of candidate surrogates will assume a basic form of discrete (Boolean) events. Counts are made of both crashes and surrogate events over road seg- ments, and statistical models are developed for event rates per unit exposure, and hence relate these models to highway variables. In this way surrogate (crash) events are evaluated for overall fidelity to actual crashes, model parameters are derived, and relative risks are estimated. In Chapter 6, extreme value theory is applied to a surrogate in the form of a continu- ous variable. Both types of surrogates are useful and continu- ous surrogates may easily be converted to Boolean form via a threshold shown in Equation 4.1: {= >1 if0 otherwise (4.1)X x a where x is the continuous surrogate and X is the resulting Boolean one. Typically x is not used as a realistic surrogate until a threshold is applied (for example, the deviation from lane center may be continuously monitored; x may be used as a crash surrogate when it exceeds a defined threshold). In general, multiple variables may be combined as shown in Equation 4.2: {= > > >1 if , , . . . ,0 otherwise (4.2)1 1 2 2X x a x a x ap p (Here all xi > ai are required to hold, but more complex logi- cal relationships are also possible—for example, by using the OR operator.) It is clear that a very large number of candidate surrogates may be generated in this way. According to the research hypotheses, it is intended to cap- ture aspects of crash mechanisms in the surrogate, in the form of disturbed vehicle control by the driver. For road departure crashes this clearly relates to lateral (steering) control, so vari- ables such as lane deviation and steering correction come to mind. Also, driver assistance systems—on suitably equipped vehicles—are designed to give alerts when an apparently high-risk scenario occurs; in the NDD (Chapter 3), such an alert was available as a candidate surrogate. Table 4.1 provides a list of basic candidate surrogates formulated, or at least ini- tially considered, in the research project. Table 4.1 is not a complete list. Indeed, given the oppor- tunity to combine basic variables via algebraic and logical functions, the full list is actually infinite. Even when this table was used, it was not considered feasible to analyze all listed surrogates in depth, because of constraints on time as well as feasibility in some cases. The list is briefly reviewed below to explain the main aspects. The first two aspects, lane departure warning (LDW) and curve speed warning (CSW) events, were recorded from the equipped vehicles used in the naturalistic driving study. Onboard systems used a lane-tracking camera, side-pointing radar, and a high-resolution digital road map, as well as vehicle variables such as turn signal, speed and steering angle, to com- pute (1) a warning that the vehicle is about to leave the lane when apparently the driver does not intend to do so and (2) a warning that the driver is approaching a curve too fast. While the full details of the algorithms are not published, it can be stated that most relevant aspects of these warning events can be reconstructed in postprocessing (motivating virtual lane departure warning [VLDW]). A virtual curve speed warning is not included in the list but is also feasible. However, it is worth noting that LDW makes use of the side-pointing radar to adapt the warning threshold. An estimate of “available maneuvering room” is made, so the event threshold is reduced when a crash barrier or an adjacent vehicle in detected by the radar, making a warning more likely. This aspect is not so easily incorporated into a post-hoc VLDW surrogate. The next candidate, lateral deviation (LDEV), simply mea- sures the instantaneous deviation from the lane center. This C h A p t e r 4

13 deviation is based on estimates from the vision-based lane tracker on the FOT vehicle, measuring the offset of the vehicle from the center of the lane. Applying a threshold to this (see the next section for more detail) may indicate some aspect of disturbed lateral control, but this ignores the way that drivers may knowingly or deliberately cut across lane boundaries. Indeed, this consideration was included in the LDW event algorithm, offering more lateral freedom when no “hard” objects were detected by the side radar. An improved measure of lane-keeping error is offered by pre- dictive lateral deviation (PLDEV), where the vehicle path is extrapolated according to a horizon time (e.g., 1 or 2 s) so that even if the vehicle is outside the lane boundary, the intent is to control or reduce the excursion. This presum- ably differs from an unintended drift out of lane (or drift toward the pavement edge), so an improved measure of control disturbance may result. Time to lane crossing (TTLC) is somewhat similar to PLDEV. Given the current trajectory of the vehicle and assuming no change of speed or steer angle (and hence path curvature), TTLC is the estimated time for the rel- evant front wheel to cross the lane boundary. As a potential risk measure, its reciprocal—inverse time to lane crossing (ITTLC)—is perhaps preferred; in this case, a large value indicates proximity to lane departure, so “big is bad.” On the other hand, when thresholds are used to define surrogate events, it is clear that the two variables are completely equiv- alent. Also, if the departure is referenced on the appropriate road boundary—so typically the shoulder width is included in the calculation—the corresponding measures are time to edge crossing (TTEC) and inverse time to edge crossing (ITTEC). The above measures are based on relatively simple vehicle kinematics relative to the lane or road edges. In an attempt to overcome some of these limitations, YRE is defined as a mea- sure of steering correction required to remain within the lane boundaries. The difference may appear minimal, but as will be developed later, this measure appears to offer numerous important advantages, the most important of which is that it infers a physical reference for an actively engaged driver to follow. The result is a criterion that is likely to be more directly related to the control task for lane keeping, some- thing that is taken up in more detail in Chapter 7. In a related finding, if control input (steering) and reference (e.g., YRE or LDEV) are estimated, the quality of driving control perfor- mance may be inferred by a statistical relationship between the two. Because this relationship may not be instantaneous (e.g., the steering may exhibit a delayed or predictive response to a path or yaw error), a dynamic relationship is better con- sidered, as, for example, in the form of a frequency-based measure of coherency, as broadly described in the control loop coherency (CLC) surrogate. Table 4.1. Summary of Candidate Surrogates Name Abbreviation Type Brief Description Lane departure warning LDW Boolean Warning from lane departure warning system (RDCW project) Curve speed warning CSW Boolean Warning from curve speed warning system (RDCW project) Virtual lane departure warning VLDW Boolean Kinematic condition based on postprocessing, aimed to emulate an onboard LDW system Lateral deviation LDEV Continuous Lateral deviation of vehicle from the lane center Predictive lateral deviation PLDEV Continuous Predicted LDEV based on current motion and lane geometry Time to lane crossing TTLC Continuous Estimated time for the vehicle to leave travel lane, given the current speed, position, and direction of motion Inverse time to lane crossing ITTLC Continuous Reciprocal of TTLC Time to edge crossing TTEC Continuous As TTLC, but including shoulder width Inverse time to edge crossing ITTEC Continuous Reciprocal of TTEC Yaw rate error YRE Continuous Correction required to current yaw rate to avoid a deviation from the lane (with a given time horizon) Control loop coherency CLC Continuous Signal processing-based measure of coherency between steer angle and LDEV variable Visual interruption VINT Boolean Driver looks away from the road for more than a specified time Steering rate QSR Boolean Steering rate below a prescribed threshold Yaw deviation associated with a boundary discontinuity YD-BD Boolean Association of lane or road boundary discontinuity (e.g., missing lane marker) with a lateral or yaw deviation

14 The final three surrogates in Table 4.1 are more relevant to using combinations of candidate variables. Visual interruption (VINT) assumes that direct eye tracking (or at least head pose) of the driver is measured. In this case, when VINT is coinci- dent with some other variable such as YRE, a surrogate event of “poor directional control while distracted” is motivated. Simi- larly, if the steering rate drops to near zero at the same time an YRE threshold is exceeded, the implication is that the driver is not responding appropriately to a yaw deviation. In a similar fashion, yaw deviation associated with a boundary discontinu- ity (YD-BD) indicates a yaw deviation associated with a break in the lane or road boundary. Presuming an increased probabil- ity of a missing or ambiguous reference for the driver causing the yaw excursion, this deviation provides another (bivariate) surrogate measure. Specific Surrogates Used for Analysis As mentioned earlier, it has not been possible to fully ana- lyze all the above surrogates within the scope of this research. In the case of driver eye tracking or head pose, the required information is not directly available in the NDD. This study focused on a subset of these surrogates, and in the next sec- tions the research team considers various aspects of LDW, LDEV, TTLC, TTEC, YD-BD, and YRE. In particular, the sta- tistical analysis of LDEV, LDW, and TTEC events is presented in Chapter 5, so further details are now presented regarding how these events were defined. LDEV The vehicle offset was obtained at a rate of 10 Hz when the subject vehicle was in a lane with a solid right or left bound- ary, and lane-tracking confidence was 70% or higher. Periods of time when the turn signal was on were excluded, and only time intervals when the lateral velocity was in the direction of a solid lane boundary were used. The vehicle offset was calculated for the above conditions for both the right and left boundaries for the entire driving data set, and the 95th global percentile value of LDEV was obtained to be used as a thresh- old for identifying LDEV events. An LDEV event was defined as the incident when a vehicle exceeded the 95th percentile lane offset. At that time, to avoid multiple repetitions during the same event, the comparison (of offset against the 95th percentile) was suppressed for 10 s in the drive record, and then resumed. For example, if a vehicle offset greater than the 95th percentile was detected, the LDEV count increased by 1. The next comparison of vehicle offset would occur 10 s later in the vehicle’s time history. LDW In the FOT study that generated the NDD, the LDW was trig- gered when the predicted vehicle path was to cross a solid lane boundary (edge or centerline), or dashed line boundary into occupied space. The vehicle had to be traveling on a road that was not a local street, the vehicle speed had to exceed 25 mph, there was no turn signal or braking in the past 5 s, and there was actual tracking on the boundary to be crossed. There was also a restriction on high steering rate in the past 5 s. The circum- stances of each LDW event in the naturalistic driving database were processed, so that only LDW events of solid right and left boundaries were retained. On the basis of the full data set, the average duration of the LDEV events was 0.61 s and the max- imum was 8.9 s. A 10-s delay prevented the long events from artificially increasing the event count and excluded only 2.3% of the NDD. TTEC TTEC was extracted on the basis of position and velocity information. Unlike YRE (Chapter 7), TTEC did not directly include curvature of the road or the vehicle path. It was calcu- lated as the quotient of the distance to the outside edge of the roadway (i.e., outer edge of shoulder) divided by the lateral vehicle velocity, as shown in Equation 4.3. ( ) = + TTEC AMR V (4.3) lateral d This measure takes advantage of a variable in the NDD, called the available lateral maneuvering room (AMR), which was derived from side-radar reflection, and lane-tracking infor- mation (Figure 4.1). The distance to the road edge was determined from the vehi- cle’s position in the lane (from the vehicle offset from the center Figure 4.1. Illustration of TTEC.

15 The 5th percentile global value of TTEC was also determined and used as a threshold to define TTEC events for statistical modeling. A TTEC event was defined as an instance when the vehicle’s TTEC was less than the 5th percentile global TTEC value. At that time, the comparison of TTEC against the 5th per- centile value was suppressed for 10 s to prevent the long events from inflating the surrogate counts. This procedure generated the number of TTEC events for each directional segment in the analysis database. of the lane following the same method as used for LDEV), the width of the vehicle, and the available maneuvering room. Only periods of driving were considered when the lateral velocity points toward the right solid lane boundary with lateral velocity to the right. To be included, a driving period had to have track- ing confidence 70% or better, and no turn signal. TTEC values were obtained for a rate of 10 Hz for all driving periods in the database that satisfied the above conditions. TTEC values in this form were used in the extreme value analysis.