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Publication Number: FHWA-HRT-08-019
Date: November 2007
Development of a Driver Vehicle Module (DVM) for the Interactive Highway Safety Design Model (IHSDM)
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SECTION 4. VERIFICATION, CALIBRATION, AND VALIDATION OF THE DVM
This section describes the verification tests performed on the DVM. The calibration/validation methods and results are described for the passenger vehicle and the heavy vehicle.
Verification tests performed on the individual modules of the DVM are described in this subsection. Some of these tests were performed on isolated modules. Because of the complexity of the driver model, however, much of the testing of individual models was necessarily performed via simulations of driving tasks using the full DVM. Particular emphasis is given to the speed and path decision modules, which we consider to be the most critical elements of the model from a safety standpoint. Sequentially considered in the following are: Perception, Speed Decision, Speed Control, Path Decision, and Path Control, as well asOutput Data Processing.
Perception is modeled as a noisy incremental process. Whenever the driver updates an available estimate, the new estimate consists of the true simulated variable potentially corrupted by both a bias factor and additive zero-mean white Gaussian noise. The bias factor is intended to account for a consistent over- or underestimation of the variable, such as a tendency to underestimate vehicle speed. For example, a bias of 0.9 represents a 10 percent underestimation of the magnitude of the variable, 1.1 represents a 10 percent overestimation, and 1.0 represents the lack of a consistent directional error. In general, a zero-mean Gaussian random noise process is added to the perceived variable to account for both the effects of perceptual resolution limitations (e.g., thresholds), and for uncertainties that tend to scale with the magnitude of the variable. Noise processes are modeled as a Gaussian white noise shaped by a first-order filter that limits rates at which instantaneous estimation errors can change over time.
The following features of the perception module have been tested:
The bias feature was verified through a test of the complete DVM. A model run was conducted in which a bias of 0.85 was associated with estimation of own-vehicle velocity, with all perceptual variables specified to be noise free. A desired free speed of 27 m/s was specified. Analysis of the results showed that the estimate of speed was consistently 0.85 times the actual speed.
Normality and Whiteness
Tests of normality and whiteness were performed directly on the simulated noise generator. Ideally, the power density function (PDF) should be Gaussian, and linear correlations among noise samples should be zero (i.e., the process should be white).
Visual inspection of the PDF of the noise samples revealed a process that very closely resembled a Gaussian noise process. Correlations among noise samples were relatively small but, as indicated below, not inconsequential.
Tests of predicted standard deviations were performed on the perception module in a standalone mode. Measures were made for all variables of interest. Results were mixed. Most predicted standard deviations were very close to the expected values, but others differed from expected values by as much as 15 to 20 percent. Theoretical analysis suggested that these discrepancies were the result of the small degree of nonwhiteness inherent in the random noise generator. Fortunately, this error in the perceptual noise standard deviation was considered unlikely to degrade the use of the DVM as an engineering tool, and no attempt was made to search for a more error-free noise-generation algorithm.
The speed decision module determines both speed and speed changes. Specifically, it determines the desired steady-state speed for situations where the driver wishes to travel at a constant speed and the deceleration and acceleration profiles when the driver needs to change speeds. Desired steady-state speed is determined by one of the following parameters:
Requirements to reduce speed include:
The driver increases speed towards the currently desired speed when there is no longer a need to travel at a lesser speed.
The speed decision module contains the following alternative user-selected treatments for driver behavior in situations in which the SD is less than the stopping distance:
These features were all tested using the full DVM as described below.
Testing the capability of the model to obey speed limits and keep steady-state vehicle speed at or below the assumed free speed was performed using a simulated tangent section containing the series of posted speeds shown in Table 3 . The driver's assumed free speed was 27 m/s.
The following qualitative behavior is expected from the model:
Figure 8 shows that this expected profile is followed closely by the DVM. Over- or undershoot in speed observed just before reaching steady-state speed is a result of the lack of anticipation built into the speed decision module as discussed earlier.
Figure 8. Effects of posted speed on predicted speed profile.
Steady-state speed in a curve depends on whether the driver is assumed to attempt to maintain lane center or to cut the curve by tracking to the inside. In the latter case, the driver is assumed to follow a curved path having a virtual radius that is greater than the geometric radius.
Verification was performed on the original model of speed in a curve in which the expected speed at curve entry is based on the assumption that the driver attempts to negotiate a curve at a speed equal to the lesser of (1) the preferred free speed or (2) the speed that yields the assumed maximum tolerable lateral acceleration. The expected curve entry speed Vce is thus:
ayo is the tolerable lateral acceleration, and
R is the geometric radius of curvature if the driver is assumed to maintain lane center, or the virtual radius if the driver is assumed to cut the curve.
Figure 9 shows the predicted speed profiles for negotiation of a highway having a simple curve of radius 75 m and total deflection of 20 degrees beginning at station 400. The virtual radius associated with curve cutting for this road is 120.3 m. The speeds at curve entry shown in figure 9 are very close to the theoretical values of 13.5 m/s and 17.3 m/s computed for the assumptions of maintaining lane center and cutting the curve, respectively.
Figure 9. Speed profile for approach, negotiation, and exit of simple curve.
Because of the lack of anticipatory behavior, the speed decreases a few tenths of a meter per second after curve entry.
The initial increase in speed observed for the case of curve cutting arises from the fact that the initial speed is based on the requirements of the geometric curve. Once the simulation starts, the speed decision in this example is then based on the virtual curve.
Verification has since been performed on the current model of curve speed shown in equation 10.
A 20 percent tolerance is built into the decision to react to an overspeed once in the curve. That is, the driver will tolerate a curve negotiation speed that results in a lateral acceleration that is 20 percent greater that the allowable value. If the magnitude of the lateral acceleration exceeds more than 1.2 times the nominally allowable acceleration, a deceleration greater than the nominally preferred deceleration is applied until the speed is reduced sufficiently to be within the acceptable range. The maximum deceleration is a user-specified parameter.
This feature of the speed decision algorithm was verified via a model run in which the bias on own-vehicle speed was set to 0.85. This resulted in the vehicle entering the curve at 1/0.85 = 1.176 times the speed that would result in the assumed preferred lateral acceleration. Because lateral acceleration is proportional to the square of the velocity, the lateral acceleration at curve entry was 1.38 times the preferred value, which was seen to trigger the larger deceleration command.
When not reducing an overspeed in a curve, the driver is assumed to examine the road ahead for highway geometric elements and traffic controls that require the driver to slow down or stop. The driver computes, for each such event, the constant deceleration that would bring the vehicle to the desired speed at the desired location. If the maximum deceleration so computed is greater than the nominally preferred value, the deceleration command is given to the speed control module. Otherwise, the currently desired speed is maintained or, if the desired speed is substantially greater than the current speed, an acceleration command is given.
The deceleration ax computed for each event requiring a speed reduction is:
V is the current vehicle velocity,
Ve is the desired velocity associated with the event, and
D is the distance to the event.
Conversely, the distance at which an initial acceleration command will be given to the speed control module is:
where axo is the nominal (threshold) deceleration.
The speed reduction properties of the DVM were verified in a number of test cases. Illustrated here is a test case using a simulated highway with a reverse curve having the properties shown in Table 4 .
Assuming a preferred acceleration or deceleration of 0.5 m/s/s, the following behavior is predicted from equations 39 and 40:
Because the second curve is substantially sharper than the first curve and follows closely after the end of the first curve, the deceleration for the second curve is expected to begin before the first curve is exited.
Figure 10 shows that the DVM predicts a speed profile that is very close to the expected behavior. The major discrepancy between theory and DVM predictions is that the deceleration begins around 20 m after expected and the deceleration reaches a magnitude slightly greater than the preferred deceleration.
Figure 10. Speed profile for closely-spaced reverse curve.
This behavior does not reflect an error in coding but is a consequence of the linear models used in the speed control algorithms as discussed earlier. When approaching the first curve, the DVM commands a deceleration at station 71 as expected. Because of the time required for the driver to release the throttle and apply the brake, the vehicle continues to accelerate for a short distance after the command is issued. Because the vehicle has not immediately begun the desired deceleration, the DVM computes a somewhat larger deceleration requirement at the next simulation interval. The commanded deceleration subsequently reaches a steady value which, of necessity, must be slightly greater than the preferred deceleration. This somewhat larger than preferred deceleration is in order to reach the desired speed at curve entry.
Figures 8 -10 are consistent with proper operation of the speed control module. This is clear because the decision and control modules must be performing properly in order to obtain the expected speed profiles. To further test the speed control module, and to test the ability of the DVM to handle grades in a reasonable manner, an additional test was performed using a simulated highway having a grade profile shown in Table 5 . Vertically curved segments of 100 m each allowed smooth transitions between the tangent segments shown in the table. This test road had no horizontal curves.
For the vehicle speed specified for this simulation (27 m/s) the transition from a flat road to a -5 degree grade began at about 14.4 seconds into the simulation, and the subsequent transition to a level road began at about 32.8 seconds.
Figure 11 shows the throttle and brake responses to the two transitions. Of note, the throttle response occurring at the beginning of the simulation arises from the initial slight loss in vehicle speed due to the way the vehicle model is initialized.
Figure 11. Effect of grade changes on model predictions: Pedal deflection.
As the road transitions to a -5 percent grade, the throttle smoothly decreases to zero and the brake is shortly thereafter applied. (Recall that the transition time between pedals is set to a negligible value because of the lags built into the linear control strategy.) The brake response-which is scaled so that it may be shown concurrently with the throttle-exhibits a single overshoot and settles smoothly to the steady value appropriate to the grade. Upon transitioning to a level road, the brake is smoothly released and the throttle settles to the original steady value after a slight oscillatory response. Both the brake and throttle responses are consistent with good linear control behavior.
Figure 12 shows that speed was regulated to within about 0.7 m/s of the desired value for this example.
Figure 12. Effect of grade changes on model predictions: speed.
The path decision module generates a commanded path behavior reflecting assumptions concerning the driver's cornering strategy. If the driver is assumed to effectively flatten a horizontal curve by cutting the curve (tracking to the inside), this module generates a commanded path that approximates an idealized circular path through a curve with a larger radius of curvature than the geometric curve. As discussed previously, curve cutting was implemented by applying correction terms to the path error (i.e., deviation from lane center), drift, and yaw-rate error. The vehicle is commanded to track center of the lane when the driver is not assumed to cut curves or is not in the vicinity of a curve.
The ideal path to be followed is either lane center, when the driver is assumed to always intend to maintain lane center, or the lane deviation described by the theoretical path correction term. Because of lags and other realistic physical limitations of the driver's control behavior, we cannot expect these ideals to be met perfectly. Because of the complexity of the driver model, however, we do not have a theoretical basis for predicting precisely what the lane deviations should be, other than by running the DVM. Verification of the path decision module, therefore, is based on the extent to which the predicted lane deviations differ from the ideal when the driver has good information (i.e., no perceptual noise or bias). If these deviations are small relative to the maximum lane deviation that allows the wheels to remain within the lane (one-half the lane width minus one-half the vehicle width), we conclude that the DVM is performing the required task of effective lane tracking and that the module may be considered to be verified.
Figure 13 shows the predicted path profiles for the two conditions represented above in figure 9: keeping lane center or cutting the curve for a single curve of radius 75 m and 20 degrees total deflection. The abscissa is expanded to highlight the section of the road containing the curve where lane deviation is expected to be nonzero. Deviation from the ideal paths for both assumptions are on the order of 0.1 m in the curve. Following curve exit, where the vehicle is expected to be near lane center, the maximum predicted lane deviation is around 0.075 m for the keep-center assumption and around 0.15 m for the curve-cutting assumption. We interpret from these relatively small errors that the combination of the path decision and path control modules are working as expected.
Figure 13. Effect of lane-keeping assumption on predicted lane deviation.
Figure 13 test results are consistent with proper operation of the path control module. Two additional tests were performed on this module. First, values of the four control gains computed in this module were examined to verify their correspondence with the values obtained by hand calculations. Second, a simple constant-speed, path-correction task was simulated to verify that the response time was consistent with the effective response delay based on theoretical calculations. These additional tests, together with those described above, supported the proper operation of speed control.
Output Data Processing
The DVM currently produces two output files. One file is a frame-by-frame recording of key system variables, including vehicle states, driver controls, highway parameters, and the driver's estimates of key system states. If multiple trials are performed in a single session, the data from each trial are stored back-to-back in the same file. The other file contains summary performance statistics, consisting of probabilities of exceeding specified limits for selected performance variables.
Validation of all the output was conducted by comparisons with manual calculations. On the basis of the data contained in the frame-by-frame recordings, hand calculations were performed on the data provided in a session of a few trials to verify the computations of means, standard deviations, and the probabilities extrapolated from these calculations. The statistics contained in the summary performance file agreed with these calculations.
Test Software Implementation for the Heavy Vehicle
This section describes the methodology and results for the test software implementation for the heavy vehicle. There were three key objectives in testing the DVM:
Seven design scenarios were developed to test the software implementation of the functional specifications for the heavy vehicle. The testing utilized these scenarios to test the boundaries of the DVM through application of real-world design problems, such as curve-cutting problems, superelevated roadway segments, or unusual driving speeds. Each scenario consists of at least one design issue, or potential problem area, that may be flagged by the DVM.
The following assumptions were made for all of the scenarios:
Design vehicle = WB-19 (WB-62)
Roadway type = Two-lane rural highway
Lane width = 3.6 m (12 ft)
Design speed = 90 km/h (55 mi/h)
emax = 8 percent
Shoulder width = 2.4 m (8 ft)
Each scenario was tested using the stochastic analysis to explore the likelihood that drivers would run into certain loss-of-control problems since the testing focused on whether or not drivers run into certain loss-of-control problems at the "trouble spot" in each scenario. The stochastic analysis allowed us to run 30 random drivers of each driver type through each highway scenario. (The deterministic analysis would have been appropriate in a comparison of alternatives analysis, since the same driver-or a driver with the same characteristics-would be navigating the highway segments being compared.)
During the simulation, the DVM tracks several aspects of the vehicle's performance, which can be viewed in the raw output data, and then produces a report that shows whether any of the following measures of effectiveness (MOEs) have indicated a potential safety problem at any point along the roadway:
Depending on the specific problem (or trouble spot) presented in each scenario, one or more of the MOEs listed above may be expected to be flagged by the DVM. The output report presents graphs of these MOEs using the mean value of all 30 drivers run in the stochastic model, as well as graphs of horizontal and vertical alignment, K-value, lateral acceleration, and vehicle speed. The report also provides a table that indicates the stations where any of the given MOEs exceed threshold values that warrant a yellow or red flag.
The following four driver types were used in the testing of each scenario:
For each of the seven scenarios, 30 simulation runs were performed using each of the four driver types, for a total of 120 simulation runs per scenario. As one might expect, the simulation runs involving either the aggressive-center or the aggressive-cutcurve driver generally resulted in more extreme values for the various MOEs. In general, the aggressive drivers typically ran the simulation 10 to 15 km/h (6 to 9 mi/h) faster than the nominal drivers, waited longer to decelerate for changes in roadway alignment, and did not reduce their speed as much through horizontal curves. The center drivers were programmed to stay in the center of their lane as they navigated curves, while the cutcurve drivers were allowed to deviate from the center path in order to increase the radius of their curve path and maintain a higher speed. No alerts in the form of yellow flags or red flags were generated from any of the simulation runs involving the nominal driver types. Therefore, the results presented in the next section are based on simulation runs involving either the aggressive-center or the aggressive-cutcurve driver type (whichever one produced the more extreme values for the MOEs).
Scenario 1: Sharp Horizontal Curve at the Bottom of a Steep Downgrade
The DVM assumes that vehicles will be able to brake as needed and that drivers will be alert and attentive. That is, the DVM is not programmed to simulate brake failure or the type of excessive truck speeds that could occur along a steep downgrade. If a driver can see a horizontal curve, the driver will perceive and react to the alignment change in time to make appropriate adjustments to his speed to safely negotiate the curve. As such, vehicle speeds did not increase along the downgrade and, therefore, the DVM did not predict a safety problem resulting from the sharp horizontal curve.
The aggressive drivers approached the curve at a higher speed, decelerated more abruptly just prior to the curve, and traveled through the curve at a higher speed than the nominal drivers. The flag that was generated for Friction Ratio X in both the original and modified scenarios is consistent with the quick deceleration. The rollover index, lane position, and Friction Ratio Y remained within tolerable limits.
Scenario 2: Series of Horizontal and Reverse Curves
The DVM generally performed as expected in that it flagged areas of excessive lateral and longitudinal friction and undesirable lane positioning for one or more of the horizontal curves. The intention in developing scenario 2 was to create a situation that potentially violated driver expectancy by following one curve with another curve in the other direction, rather than following it with a tangent, and in come cases following a horizontal curve with a curve that has a smaller radius. However, inherent in the DVM programming is the inability to surprise a driver. That is, as long as there is sufficient SD, it is not possible to surprise a driver with an upcoming horizontal curve. It is assumed that if the driver can see the curve ahead, the driver will perceive and react to the curve and make appropriate adjustments to his or her speed in order to safely negotiate the curve.
The aggressive drivers maintained a greater speed throughout the roadway and decelerated more abruptly when reducing their speed, resulting in more extreme values for lateral skid index and lateral acceleration than the nominal driver.
Scenario 3: Single Horizontal Curve with Insufficient Superelevation
As expected, the lack of superelevation on a horizontal curve results in greater friction ratios-both lateral and longitudinal-which increase as the curve radius is decreased. The results of the center driver type were presented because they were more extreme in this scenario than the cutcurve driver, which makes sense given that the cutcurve driver can avoid the negative superelevation by cutting across the centerline of the road. A few unexpected results with this scenario include:
Scenario 4: Long Tangent Followed by a Sharp Horizontal Curve
The assumption behind testing this scenario is that a driver might become distracted or complacent during the long tangent and then be surprised by the sharp curve, exhibiting a delayed reaction and an improper assessment of the necessary adjustment in speed. However, the DVM cannot test for violation of driver expectancy, which was the sole purpose of this scenario. Even so, the DVM did generate flags at the beginning of the horizontal curve where one would expect there to be safety issues. The element of surprise could be simulated by defining a new driver configuration in which SD is severely limited. This option was not explored here.
Scenario 5: Single Horizontal Curve with Sight Obstructions
The objective of this scenario was to limit horizontal SD throughout a horizontal curve and determine its effect on driver behavior. The results of the simulation suggest that the driver has little difficulty and is able to negotiate the horizontal curve as though there were no horizontal sight obstruction. The SD values in the raw output data file indicate that the driver has unlimited SD before entering the horizontal curve; however, it is difficult to confirm these values without the benefit of a 3-D model or a site visit.
Scenario 6: Insufficient Lane Widening at a Horizontal Curve
The purpose of this scenario was to determine whether the additional pavement width provided in the horizontal curve would affect the driver's path, measured by lateral offset. The results suggest that the additional pavement width had no impact on the driver's path.
Scenario 7: Horizontal Curve Beginning Beyond the Crest of a Vertical Curve
The objective of this scenario was to surprise the driver with a horizontal curve just beyond the crest of a vertical curve. Limiting SD appears to be the only method within the DVM of surprising the driver. The results of this scenario show that the driver has to decelerate very suddenly after the crest of the vertical curve in order to safely negotiate the horizontal curve. This rapid deceleration corresponds to the downward spike in Friction Ratio X (longitudinal skid index). The driver has a lateral offset towards the outside of the curve before he is able to regain his intended path and cut to the inside of the curve, which is consistent with the driver not expecting the horizontal curve.
This section presents the overall conclusions and addresses the three key objectives from the DVM testing. It also identifies potential functional revisions that may be considered in future enhancements. The scenarios presented were developed and evaluated using version v3.02c-070327, which was the most current version available when the work for this task began. The research team recognizes that updates made to the software since that time may have addressed or negated some of the issues presented in the discussion here.
Objective 1: Evaluate whether the DVM functioned and ran as it was designed.
The DVM operated as it was designed. However, it did not always yield intuitive results. For example, none of the seven scenarios generated flags when the nominal driver type was used. This was somewhat surprising given the extreme alignment and/or problematic situation present in the scenarios. When the aggressive driver type was used, the DVM generally triggered flags at locations where the vehicle had to quickly decelerate to successfully navigate the roadway, such as at the beginning of a sharp horizontal curve. These locations are, in general, the same locations where we would expect vehicles to have problems navigating the roadway if the driver did not decelerate sufficiently. The DVM assumes, however, that the drivers are able to determine the appropriate curve speed if they can see the start of the curve. Whenever curve entry points were visible, the drivers were able to reduce speed appropriately when approaching the curve.
The Friction Ratio X variable is the most commonly flagged variable, and is typically flagged when aggressive drivers are quickly reducing their speed to negotiate a horizontal curve. Friction Ratio Y generally followed the shape of the lateral acceleration graph and was only flagged in scenarios 2, 3, and 4. An alert was produced in scenario 2 at the node of a reverse curve; in the modification of scenario 3, the alert was produced at the start of the curve with no superelevation; and in scenario 4, the alert occurred throughout the length of the curve. In scenarios 2 and 3, these results were expected, but it is unclear why Friction Ratio Y was so much higher in scenario 4 than in other scenarios with curves of the same radius and drivers traveling at the same speed. Lateral offset was rarely flagged, but appeared to be triggered when a vehicle deviated from center by more than 1 m. The locations where this occurred were reasonable and expected. Rollover index was never flagged, and it is unclear what threshold values would create a rollover alert. However, the truck parameters were for an unloaded truck. An analysis of a fully loaded truck having a significantly higher center of gravity might trigger some rollover flags.
Objective 2: Note functional revisions that would improve the DVM.
When the scenarios were initially developed, the expectation of a safety problem being present was based, in many cases, on surprising the driver. However, it was noted that the element of surprise cannot be programmed into the DVM. That is, violation of driver expectancy per se is not something that the DVM will flag. Therefore, the flags that were generated in testing the scenarios were potentially influenced more by the characteristics that make up an aggressive driver (e.g., waiting until the last possible moment to decelerate, driving fast through curves) than by the alignment itself.
Currently, there are several driver options to choose from when running the DVM evaluation. While experienced users may eventually design their own drivers, the average user will probably choose from a few standard drivers available on the screen. The user should be able to view a brief description of the driver type when making this choice.
Objective 3: Identify other areas of improvement to the presentation of the DVM output reports.
In testing the scenarios, several limitations (or areas of improvement) from a user-friendliness standpoint were noted and are presented below:
Calibration/Validation of the Passenger Vehicle
The calibration/validation process consisted of six basic iterative steps:
Step 1.Collect on-road and, where supportive, whole-task simulator data to allow testing of certain basic assumptions and to provide a basis for calibrating the independent model parameters.
Step 2. Review psychophysical literature to determine reasonable ranges of values for independent parameters.
Step 3. Perform model sensitivity analysis to determine which parameters can be assigned default values and which need to be adjusted to reflect different driver types.
Step 4. Calibrate the model by adjusting parameters to provide a match to the experimental data.
Step 5. Compare predicted and observed behavior to test assumptions and revise the model as necessary to improve the correspondence between model predictions and experimental data.
The sixth and final step involves the use of "holdout" data to validate the model and required the team to:
Step 6. Compare predicted and observed behavior to test assumptions and revise the model as necessary to improve the correspondence between model predictions and experimental data.
Table 6 and Table 7 summarize the results of the validation testing for, respectively, the tests of critical assumptions and tests of real-world predictive abilities.
Parameters for the Passenger Car Driver
Two classes of driver parameters are discussed: those relating to driver preferences that are presumably under the control of the driver to a large extent, and those relating to driver limitations (primarily perceptual variability and biases) that are presumably not under the control of the driver. These parameter classes are discussed separately after a brief review of data sources. Parameters are quantified for two driver types: the average driver and the 85th percentile driver, which correspond respectively to the nominal and aggressive drivers represented in the standard DVM driver configurations.
Basis for Selecting Parameter Values
Key driver parameters distinguishing the driver types were calibrated from the data obtained in the Battelle on-road study.(3) Not all parameters were or could be defined in this manner, however. The following information sources related to human performance were relied upon to define the full set of parameters:
Whenever the driver updates the estimate of a particular variable, the new estimate consists of the true simulated variable potentially corrupted by both a bias factor and additive zero-mean noise as discussed previously. Noise processes are modeled as a Gaussian white noise shaped by a first-order filter that limits rates at which instantaneous estimation errors can change over time.
Representative values for noise terms are discussed individually below. Before presenting these details, let us first review the general principles developed for selecting parameter values.
The following approach to selecting independent driver-related model parameters is based partly on previous studies of human perception and on model sensitivity analysis as discussed above. It is consistent with the DVM's primary goal of developing a tool that will allow the highway designer to explore the effects of highway geometry on speed behavior.
Parameters related to driver limitations were quantified as follows:
A number of tolerances are available to reflect the allowable errors in various quantities. A speed tolerance is provided, and two such variables are provided for acceleration: one when attempting to regulate about zero acceleration or deceleration, and another (typically larger) value for desired nonzero accelerations. These model parameters have not been calibrated against data. Until such calibrations are performed, we recommend that these variables be set to zero.
The remaining (nonzero) parameters are reviewed below. The three parameters that distinguish between the nominal and aggressive driver-lateral acceleration factor, nominal longitudinal acceleration, and free speed-are discussed in greater detail further on.
Ayo is lateral acceleration in m/s/s, and
C is curvature in rad/m.
The value of 36 was found to provide a good visual match to the experimentally observed relation between implied curve acceleration and curvature.
Quantification of Driver Types
Two driver types-the average driver and the 85th percentile driver-are defined in terms of values assigned to three driver-related model parameters: free speed, lateral acceleration factor, and preferred longitudinal acceleration. Values for these parameters, which were derived from experimental data obtained in the Battelle on-road study, are given in Table 8 ; their derivation is described below. Other driver-related parameters remain as indicated above.
The average free speed for each of the 18 subjects participating in the on-road study was determined by averaging the four highest speed peaks observed in the speed profile over the entire test run. The mean and standard deviation of these 18 averages were used to estimate the 85th percentile free speed on the assumption of a Gaussian distribution. The estimated 85th percentile speed was computed as:
where X85 is the estimated 85th percentile value, M is the sample mean, sd is the sample standard deviation, and Z85 is the Z-value (approximately 1.037) for which the integral under the Gaussian distribution is 0.85.
The following statistics were computed for the free speed in m/s:
85th percentile 31.8
All statistics shown here pertain to the 18 within-subject averages.
Lateral Acceleration Factor
The following procedure was employed to estimate the 85th percentile value for the lateral acceleration factor K:
Standard deviations of 6.17, 5.10, and 3.97 were computed for curves 3, 5, and 6, respectively. The mean sd of 5.08, along with the estimated mean for K yielded an estimate of 41.3 for the 85th percentile value.
Preferred Longitudinal Acceleration
The deceleration on curve approach and the acceleration after curve exit both exhibited speed dependencies that were modeled as a square-root relationship between acceleration or deceleration and total speed change. Because the current model structure does not contain a reliable predictive model for total speed change, acceleration and deceleration are presently treated as a constant having a value representative of those observed in the Battelle on-road experiment.
To obtain representative statistics, the mean deceleration on curve approach was computed from all estimates of average deceleration where the total speed reduction was 2.0 m/s or greater. The average deceleration associated with a given curve approach was estimated by dividing the total decrease in speed by the time over which the driver was decelerating for the curve.
Because of the relationship between deceleration and speed change, computing the standard deviation from the entire set of deceleration measurements would overestimate the variability of the deceleration about the mean deceleration associated with a given speed change. A more representative measure of acceleration variability would be the standard deviation relative to the local mean. An approximation to this metric was obtained by adjusting the model for deceleration to provide a least-squared-error match to the observed decelerations, treat the model prediction of deceleration for a given speed change as the local mean, and compute the standard deviation of all measured decelerations about their local means. The 85th percentile preferred acceleration was computed according to equation 42 using the standard deviation about the estimated local mean.
The best-fitting model for the deceleration data was:
axo is the estimated preferred deceleration, and
D V is the required decrease in speed.
The following statistics (m/s/s) were computed for average deceleration:
85th percentile 0.62
Note that the 85th percentile value corresponds to speed decrements for which the expected deceleration is around 0.47 m/s/s (0.048 g).
Calibration/Validation of the Heavy Vehicle
Parameters related to vehicle dynamic response and driver performance limitations were quantified. Parameters remaining to be determined were:
Calibration and validation were originally proposed to be separate tasks, with a portion of the available on-road data being used to quantify the various independent model parameters, including those enumerate above, and the remaining held back to be used to test the predictive validity of the DVM using the parameter values determined in the calibration phase.
A study of driver behavior suitable for quantifying all the parameters listed above would require the following highway and operational conditions:
Such conditions, which are highly idealized and perhaps realizable only in simulation studies, were not provided by the Virginia Tech Transportation Institute (VTTI) on-road study. Speed limits on the section of highway analyzed in this study were 45 and 35 mi/h, likely preventing the drivers from reaching their preferred free speed as defined above. Because this study did not include situations where drivers were instructed to perform maximum comfortable braking or negotiate curves at maximum comfortable speeds, maximum tolerable acceleration levels could not be determined.
The highway geometry, coupled with the speed limits, did not facilitate partitioning the test road into portions separately used for calibration and validation. Consequently, the on-road data were used to jointly calibrate and validate the DVM. To be consistent with the passenger vehicle calibration/validation procedures, the ability to predict a speed profile falling within one standard deviation of the mean speed profile provided by the test drivers was selected as the criterion for validity.
Data from an on-road study comparing the behavior of drivers of a passenger car and a Class 8 tractor-trailer heavy vehicle were used during the calibration/validation process. The test route was a 16-km route consisting of Virginia State Route (SR) 114 and Montgomery County Route (CR) 685. Both routes are two-lane rural highways. The first leg-SR-114-was determined to provide insufficient challenge to provide adequate data for either calibration or validation. Accordingly, the calibration/validation results presented herein are based on the data obtained from 6.2 km of CR-685.
The drivers first drove SR-114 to the intersection of SR-114 and CR-685, controlled by a stop light, then turned onto CR-685. The intersection of the two routes is considered to be station 0 for this analysis, where one unit of station increment corresponds to 1 m proceeding generally north.
Global Positioning System (GPS) instrumentation was used both to determine the horizontal and vertical profiles on the test route and to allow recording of vehicle location during the test drives conducted in previous research(3). During the current study phase, the roadway calibration data were found to have serious internal inconsistencies. Specifically, distances between two points on various tangent sections computed from the GPS recordings differed by varying amounts from distances between corresponding points determined from the distance-measuring wheel. Because no consistent transformation between the two methods of measuring distance could be found, VTTI re-calibrated CR-685 for this study phase. GPS recordings were converted to measurements of easting, northing, and height, all in meters. The resulting records were internally consistent, and a plot of the easting and northing measurements provided a good qualitative match to a map of the test route.
In order to provide the roadway-related inputs needed for model analysis, the roadway measurements were analyzed to determine curvature and height as a function of station. East (X) and north (Y) coordinates were determined from the GPS measurements and, where there were significant gaps in the GPS recordings, from interpolations using onboard measurements of speed and yaw rate.
Engineering drawings of CR-685 provided by the Virginia DOT, Christiansburg Residency, were used to provide a first approximation to the analytic representation of horizontal profile in terms of tangents and curves of constant radius. Adjustments were then made to improve the visual match to the road as recorded by VTTI. Graphical analysis of the recording of height versus station, derived from the GPS measurements, was employed to determine the analytic representation of the vertical profile.
Figure 14 provides a comparison of the plan views of the test route as determined from the on-road calibration effort with the analytic representation used in the DVM. The match was considered adequate to allow confidence in the estimates of the radii of the horizontal curves contained in the test road. Vertical profiles of the measured and analytic test routes are shown in figure 15.
Figure 14. X/Y plot of test route.
Figure 15. Vertical profile.
The posted speed for the test route was 45 mi/h (about 72 km/h, or 20 m/s) from stations 0 to 5158 and beyond station 6067, and 35 mi/h (about 56 km/h or 15.6 m/s) from stations 5158 to 6067.
Five drivers participated in the heavy-vehicle portion of the on-road study. Data usable for model analysis were obtained from four of these drivers. Because there were occasions when other traffic impacted the behavior of the test drivers, not all replications could be used. Replications included in the database used for model calibration and validations are indicated by an "x" in the corresponding cell in Table 10.
An ensemble-averaged (mean) speed profile was computed from the results of the first usable runs performed by each subject, and a similar mean-speed profile was computed from the final usable runs. The close correspondence between the two mean-speed profiles shown in figure 16 suggested that meaningful learning of the road characteristics by the drivers did not occur during the study with respect to speed decision-making. Accordingly, further analysis was performed using mean-speed profiles computed for each driver from all usable runs.
Figure 16. Mean first and last speed profiles.
Road curvature with station is shown in figure 17. Positive curvature signifies a curve to the right. Some visual correlation between the magnitude of the curve and reduction in speed can be observed, but it should be noted that posted speed limits as well as limits on the uphill acceleration capability of the vehicle also influenced vehicle speed.
Figure 17. Road curvature.
Mean speed profiles for the four test drivers are shown in figure 18. One pair of drivers drove consistently slower that the other pair, by around 2-3 m/s, but the general trends of speed with station were similar. Figure 19 shows the overall mean speed profile along with the one standard deviation bounds.
Figure 18. Mean speed profile for four drivers.
Black: Mean profile
Gray: +/- Standard deviation
Figure 19. Mean +/- standard deviation of driver means.
As noted above, the DVM allows the user to specify whether the driver is assumed to track to the inside of the curve (cut the curve) or to attempt to maintain the vehicle in the center of the lane, where lane position is defined as the distance of the center of mass of the cab from the center of the lane. In order to provide guidelines for setting this model parameter, we need to explore actual driver behavior to determine the strategy for steering a heavy vehicle (tractor-trailer) of the type considered in this study.
By cutting the curve, the driver effectively increases the radius of curvature, thereby allowing curve negotiation at a higher speed and lower lateral acceleration than by maintaining a lane-center position throughout the curve. The effect is greatest for sharp curves with small deflection (directional change) and diminishes as either curve radius or curve deflection is increased.
While the above comments apply generally to a single-unit vehicle, the driver of a tractor-trailer must consider the location of the trailer wheels when negotiating a curve. Even with the tractor maintained near lane center, the rear trailer wheels may track so far to the inside as to cross the lane boundaries. One might therefore anticipate that heavy vehicle drivers would track to the outside of sharp curves and maintain lane center for more gentle curves.
There did not appear to be a consistent curve-tracking strategy over the 6,000 m of travel. For much of the travel the truck appeared to track on the average to the right of center independent of the horizontal geometry. There is some indication that when negotiating a reverse curve, the process of negotiating the first curve tended to set up the vehicle to track to the outside of the second curve. This may have been an intentional strategy, or it may have reflected a difficulty in steering quickly enough to enter the second curve at lane center.
The same six iterative steps used in the calibration/validation of the passenger vehicle were used to calibrate/validate the heavy vehicle. The on-road data along with model analysis were used to determine guidelines for treating curve cutting and for calibrating the driver-related parameters of nominal longitudinal acceleration and lateral acceleration factor. As noted previously, the on-road study was not conducive to determining values for free speed and maximum tolerable accelerations for the heavy-vehicle driver.
Variations in speed and lane deviation for the test route were minor. Table 11 shows the validation results for curve cutting, longitudinal acceleration, later acceleration, horizontal SD, and short tangents.
Black: Mean speed profile of four drivers
Light Gray: Mean +/- one standard deviation
Dark Gray: Model prediction
Figure 20. Predicted speed profile when reducing the lateral acceleration factor to 20.
Recommended Values for Driver Parameters
Recommended values for parameters related to driver preference are shown for both passenger car and heavy vehicle truck drivers in Table 12 for the nominal (as opposed to aggressive) driver. To the extent allowed by the data, these parameters reflect the on-road data used to produce the DVM. In the absence of definitive data, engineering judgment provided estimated values.
Validation of Vehicle Dynamics Model for Heavy Vehicle
Both the passenger vehicle and the heavy truck components of the DVM require a VDM that can simulate the full range of lateral and longitudinal movements of the vehicle including acceleration, steering, braking, power train, drive train, and tires. For the DVM, the VDANL module was used. For the passenger vehicle component of the DVM, VDANL was used without any additional calibration or validation activities. However, the VDANL code required additional validation for heavy truck modeling.
To conduct the heavy vehicle validation, project staff from Systems Technology, Inc. (STI) used the parameter and test data collected at the Vehicle Research Test Center (VRTC) on an earlier and separate National Highway Traffic Safety Administration project. The vehicle tested at VRTC was a 1992 White-GMC truck manufactured by Volvo GM Heavy Truck, model WIA64T (two drive axles), and a 1992 Fruehauf van trailer, model FB-19.5NF2-53 (53-ft-long box trailer with two axles). This tractor-trailer combination is similar to the WB-20 [WB-67] vehicle combination. This combination is similar to, but shorter than the combination used to collect the on-road data for the DVM (a 1997 Volvo VN/48-ft van trailer).
The heavy truck validation was conducted with a standalone version of the VDANL code. The parameter development and model evaluation were conducted for the empty trailer condition (VRTC conducted empty and fully loaded trailer tests). The empty trailer condition is what VRTC has presented from their evaluation and was of most interest to the current effort. A full VDANL vehicle parameter set was developed including vehicle, drive train, suspension, braking, and tire parameters. Once the vehicle parameter sets were fully developed, the model was run through maneuvers identical to those performed with the actual vehicle. The measured test driver inputs (brake, throttle, handwheel angle, etc.) were used to drive the VDANL vehicle model. The maneuvers tested covered a broad range of vehicle operating conditions, which were set to characterize the model's static and dynamic performances and were then compared to measured dynamics. The tests included slowly increasing steer, step steer, lane change, straight line acceleration, straight line braking, and several others. Some of the test data were collected with open loop driver inputs and others were closed loop. For maneuvers with open loop driver control and multiple test runs, statistical estimates of the mean vehicle response were made and used for comparison with the VDANL results.
The VDANL model evaluation for the tractor-trailer combination produced results that were consistent with those for the VRTC model evaluation (a full report on this effort was provided to the FHWA separate from this report). The parameter set should be considered representative of this heavy vehicle class but not an exact match for any particular vehicle.
In addition to validation of the heavy truck modeling within VDANL, a number of enhancements to VDANL were completed; these included: