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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

Introduction

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

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

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:

  • Proper operation of the bias feature
  • Normality and whiteness of the random noise process
  • Accuracy of the standard deviation of the noise process

Bias

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.

Speed Decision

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:

  • Driver's preferred free speed, the maximum speed at which the driver intentionally drives.
  • Posted speed, when the driver is assumed to obey speed limits.
  • Speed in a curve, determined by allowable lateral acceleration.

Requirements to reduce speed include:

  • Negotiating a curve too fast.
  • Posted speed ahead lower than current speed.
  • Stop sign ahead.
  • Requirement to slow down for a curve ahead.

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:

  • The driver is familiar with the road and knows what lies beyond. In effect, the SD limitation is ignored.
  • The driver assumes a long tangent just beyond the visual range. The driver responds as if nothing lies beyond visual range requiring the driver to slow down.
  • A maximally cautious driver assumes a stopping requirement just beyond visual range.
  • The driver assumes road geometry beyond the SD is similar to that recently negotiated. In effect, a horizontal curve of the same geometry as the curve most recently negotiated is assumed.

These features were all tested using the full DVM as described below.

Steady-State Speed

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.

Table 3. Array of posted speeds.
Station (m) Posted Speed (m/s) Posted Speed (mi/hr) Posted Speed (km/hr)
0 30 67 108
500 20 45 72
700 25 56 90
1100 30 67 108

The following qualitative behavior is expected from the model:

  • The initial speed should be about 27 m/s, despite a posted speed of 30 m/s, because the driver does not intentionally drive faster than the free speed.
  • The vehicle should decelerate such that a speed of about 20 m/s is attained at station 500 and-because the next posted speed is higher-the vehicle should remain at 20 m/s until the next posting is reached.
  • The driver should begin accelerating toward 25 m/s after passing station 700 and should stabilize at that speed until the next posting is reached.
  • The driver should again accelerate after passing station 1,100 and stabilize at the free speed of 27 m/s.

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. Line Graph. Effects of posted speed on predicted speed profile. The graph depicts the expected profile following the DVM.

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:

Equation 38. V subscript ce equals the product of ay subscript o times R, that product raised to the one half power. (38)

where

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. Line graph. Speed profile for approach, negotiation, and exit of simple curve, as described in the text.

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.

Speed Reduction

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:

Equation 39. ax equals the difference of V squared minus V subscript e squared, that difference divided by 2 times D. (39)

where

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:

Equation 40. D equals the difference of V squared minus V subscript e squared, that difference divided by 2 times ax subscript o. (40)

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 .

Table 4. Properties of the simulated reverse curve.
Radius (m) Direction Length (m) Entry Station (m)
200 Left 300 300
100 Right 100 650

Assuming a preferred acceleration or deceleration of 0.5 m/s/s, the following behavior is predicted from equations 39 and 40:

  1. The vehicle starts slowing down at station = 71 m with a deceleration of 0.5 m/s/s.
  2. Entry velocity for the first curve is about 22.4 m/s.
  3. The vehicle resumes slowing down at station = 400 with the preferred deceleration.
  4. The entry velocity for the second curve is about 15.8 m/s.
  5. The vehicle accelerates to the desired free speed (27 m/s) at the rate of 0.5 m/s.

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. Line graph. Speed profile for closely-spaced reverse curve, as described in the text.

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.

Speed Control

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.

Table 5. Simulated grade profile.
Station Grade
0-400 0%
500-900 -5%
1,000-3,000 0%

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. Line graph. Effect of grade changes on model predictions: Pedal deflection, as described in the text.

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. Line graph. Effect of grade changes on model predictions: speed, as described in the text.

Figure 12. Effect of grade changes on model predictions: speed.

Path Decision

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. Line graph. Effect of lane-keeping assumption on predicted lane deviation, as described in the text.

Figure 13. Effect of lane-keeping assumption on predicted lane deviation.

Path Control

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:

  • Evaluate whether the DVM functioned and ran as it was designed.
  • Note functional revisions that would improve the DVM.
  • Identify other areas of improvement to the presentation of the data in the DVM.

Methods

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:

  1. Lateral offset (lane position).
  2. Rollover index.
  3. Friction ratio Y (lateral skid index).
  4. Friction ratio X (longitudinal skid index).

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:

  1. Aggressive - center
  2. Aggressive - cutcurve
  3. Nominal - center
  4. Nominal - cutcurve

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).

Results

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:

  • It was expected that this scenario would be the most likely to generate a flag for the rollover index; even with the 500-m (1,640-ft) radius curve, a warning was not generated.
  • It was a little surprising that the first version of the alignment (with the 1,000-m [3,280-ft] curve) did not generate any flags.

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.

Conclusions

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[1] 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:

  • The output report shows graphs of several variables over the length of the roadway.  The graphs of vertical and horizontal alignment, vehicle speed and lateral acceleration are very helpful, but Friction Ratio X and Y are not common terms that are particularly meaningful to a highway engineer. The rollover index is slightly more intuitive, but there is no indication of what values should raise concern.  While it is obvious that a rollover index value of 0.5 indicates a greater likelihood that the vehicle will roll over than a rollover index value of 0.3, it still does not indicate what the likelihood is.  The lateral offset variable is also helpful, but it is unclear what the offset is measured from and which side of the roadway corresponds with positive and negative values.   SD would also be an important and meaningful variable that could be included in the report.
  • When an evaluation is run, the output report does not provide information about the roadway characteristics beyond the basic horizontal and vertical alignment. If roadway characteristics are modified at all (for example, the lanes are widened, object offset is changed, shoulders are added, etc.), the evaluation no longer represents the saved roadway, and there is no way to determine from the output report that these characteristics have been changed. It would be helpful if there were a way to link an evaluation to the roadway characteristics for which it was run.

Calibration/Validation of the Passenger Vehicle

Calibration/Validation Methods

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.

Results

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.

Table 6. Results of validation testing for the tests of critical assumption.
Assumption Tested Validation Results Conclusions
Some drivers attempt to track to the inside of a curve (cut the curve) to allow a larger comfortable curve negotiation speed. Drivers tend to cut curves in a manner predicted by the model. Curve-cutting elements of the DVM accurately predict driver behaviors and are retained.
Drivers attempt to negotiate all curves at speeds that correspond to their individual maximum comfortable lateral accelerations. Assumption not confirmed. Sharper curves are negotiated with higher lateral accelerations than less-sharp curves-following square root theoretical model. Square root relationship has been implemented into current DVM.
Drivers attempt to decelerate for an event with individual preferred constant deceleration.    
1.       Decelerations are relatively constant over the course of the speed reduction. 1.       Curve transiting profile data revealed one driver segment following this sub-assumption, but other segments tended to follow mixed alternatives. 1.       This conservative sub-assumption is not consistently violated, and should be retained in the computerized DVM.
2.       The preferred deceleration is independent of the amount of speed reduction necessary. 2.       A theoretically derived square-root dependency between deceleration and total desired speed change was strongly supported-with acceleration also found to follow the same relationship. 2.       Square root dependency would require a not-straightforward change in the conceptual model-and is recommended for future implementation-but not in the current version of DVM.
3.       Drivers increase speed at a constant acceleration that equals the absolute value of preferred deceleration. 3.       Confirmed for a segment of drivers earlier seen to have a constant pattern of deceleration, but other driver segments also found to employ a constant acceleration in exiting curves. 3.       Constant preferred accelerations sub-assumption should be retained in the computerized DVM.
Driver lateral-axis (steering) behavior can be adequately represented by a linear control strategy which operates on error-feedback information. Results indicate that DVM performed within tolerances, but was slower than real-world driving with respect to quick lane maneuvers. DVM provides a conservative representation of steering correction behavior-this is adequate for the intended application.
Table 7. Results of validation testing for the tests of real-world predictive abilities.
Predictive Capabilities on Real-World Roads Validation Results Conclusions
Driving performance on Washington State Route (SR) 4 Drivers had a tendency to maintain a lane center position. Curve-entry speeds are as predicted by the model, but overall curve speeds are less than predicted. Small errors in speed profile are not significant but should be addressed in future DVM development. DVM currently provides conservative results useful for geometric evaluations.
Driving performance on Virginia SR-114 (curve #2) On-road speed profiles match modeled speed to within one standard deviation. DVM adequately models real-world behaviors.
Driving performance on Virginia SR-685 (curve #10) On-road speed profiles match modeled speed to within one standard deviation. However, no curve cutting takes place. DVM adequately models real-world behaviors, when curves are relatively isolated. DVM currently provides conservative results useful for geometric evaluations.

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:

  1. Previous laboratory studies of human performance, especially those involving laboratory manual control (tracking) tasks.(4,7) Mathematical models of human control behavior developed in these studies have provided the basis for the algorithms used in the speed control and path control elements of the DVM and have also provided specific values, or ranges of values, for some of the driver-related independent parameters.
  2. Review of the perceptual literature performed under this contract provided ranges of values of variables related to perceptual limitations that were explored in a model sensitivity analysis.
  3. Model sensitivity analysis performed under this contract, which illustrated the degree to which the various driver-related model parameters would influence performance predictions and which therefore allowed us to determine which parameters needed to be calibrated and which could safely be neglected.
  4. On-road studies performed by Battelle under the previous contract. These studies provided data that allowed testing of the overall model structure and provided data useful in calibrating certain parameters.
  5. Engineering judgment. It was necessary to make educated guesses of the values for certain parameters. Years of experience in modeling and observing human controller behavior were drawn upon to estimate values that would lead to reasonable model behavior. In all cases, testing with the DVM verified that the entire set of values selected for driver-related model parameters resulted in model predictions consistent with observed behavior.

Driver Limitations

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.

  • A single time constant for noise filtering, tentatively set at 2 seconds, is applied to all noise processes.
  • Noise scale factors, thresholds, and biases are adjusted independently for estimation of current vehicle velocity and for curve negotiation velocity. The scale factors and thresholds are to be determined on the basis of realistic driving tasks and/or laboratory psychophysical experiments. The bias terms may be determined from new or published data or may serve as user-adjusted independent parameters of the model analysis.
  • A single generic noise scale factor is assigned to all lateral-axis perceptual variables and to longitudinal acceleration.
  • Thresholds associated with perception of path error and yaw-rate error are kept as independent parameters and adjusted on the basis of new or published performance data only when accurate predictions of lateral-axis behavior are desired.
  • Other than as described above, thresholds are ignored, and bias terms are set to 1.0 (i.e., no bias).

Parameters related to driver limitations were quantified as follows:

  • Generic scale factor: The noise scaling factor associated with all perceptual variables except as described below. A value of 0.1 was selected to provide path variability consistent with data obtained in the Battelle on-road study.
  • Generic filter time constant: The filtering time constant applied to all noise processes. The value 2.0 was selected based on engineering judgment.
  • Curve noise constant: The noise scale factor associated with estimation of the appropriate negotiation speed for the curve ahead. Because the driver's ability to estimate this speed is assumed to degrade with increasing distance to the curve, the corresponding noise scale factor is computed in the DVM as a curve noise constant times distance to the curve. The value of 1.0E-4 for this variable was selected to provide speed variability consistent with behavior observed in the Battelle on-road study.
  • All bias terms: Set to 1.0 by default.
  • All threshold values: Set to zero by default. Model sensitivity analysis suggests that thresholds for estimations of current vehicle velocity and appropriate curve negotiations speeds might be useful for more accurate modeling of the effects of horizontal geometry on speed decision and control. More accurate predictions of lateral-axis control might accrue from calibration of thresholds for perception of path and yaw-rate errors.
  • Velocity scale factor: Noise scale factor pertaining to estimation of own-vehicle speed. The value of 0.02 for this variable was selected to provide speed variability consistent with behavior observed in the Battelle on-road study. Note that speed variability is influenced by the combined effects of velocity scale factor and curve noise constant.
  • Distance scale factor: Noise scale factor associated with estimation of distance to target (e.g., curve entry, traffic control device). Model sensitivity analysis indicates that errors in estimating this variable have substantially less influence on driver behavior than errors in estimating vehicle speed and curve negotiation speed. This noise process has therefore been ignored.
  • Variables relating to optical expansion: The driver is assumed to use the perceived optical expansion of an object located at the desired stopping point when estimating the deceleration required to bring the vehicle to a stop at the desired location. Because the DVM has not been calibrated for these parameters, we currently have no basis for assigning nonzero values.

Driver Preference

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.

  • Obeys speed limits: A logical variable such that TRUE causes the driver to adjust speed for the posted speed limit when appropriate, and FALSE causes the driver to ignore posted speeds and adopt the free velocity (discussed below) as the preferred tangent speed in the absence of geometric or SD limitations.
  • Always keep center: A logical variable such that TRUE causes the driver to always attempt to maintain lane-center position, and FALSE allows the driver to cut the curve when negotiating a horizontal curve.
  • Road familiarity: This parameter selects among the four assumptions describe previously concerning the driver's familiarity with the road and the strategy for driving unfamiliar roads.
  • Max rate pedal: The maximum rate of brake or accelerator pedal movement, expressed as the fraction of full scale deflection per second. A value of 2.0 was selected based on engineering judgment.
  • Maximum longitudinal acceleration: The maximum deceleration (g) employed after entering a curve to correct for overspeed (not intended to represent the maximum braking available in an emergency). A value of approximately four times the nominal declaration has arbitrarily been assigned to this parameter.
  • Lateral Acceleration Factor: The variable K in the theoretical relationship between preferred lateral acceleration in a curve and curvature:

Equation 41. Ay subscript o equals K times C to the one half power. (41)

where

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.

  • Maximum lateral acceleration: The lateral acceleration (g) assumed to be maximally tolerable by the driver when negotiating a curve. The value of 0.4 was selected to be slightly greater than the maximum implied lateral acceleration observed in the data base used for differentiating driver type (discussed below). Lower values would be expected for vehicles with substantially higher centers of gravity.
  • Nominal longitudinal acceleration: The longitudinal acceleration (g) assumed to be preferred for accelerating and for normal braking. The value of 0.048 was selected as a representative value based on decelerations observed in the Battelle on-road studies.
  • Desired gain margin: A parameter of the speed-control algorithm that determines the responsiveness and degree of stability of steering control. A value of 3.0 was selected on the basis of model analysis to provide a rapid but minimally oscillatory steering response.
  • Lane margin: The minimum distance (m) that the driver is assumed to prefer between the wheels and the lane edge when cutting the curve. A value of 0.3 m is currently used.
  • Free velocity: Preferred speed (km/h) when not limited by highway geometry, traffic control devices, or SD. A value of 105 was determined from analysis of the Battelle on-road data as described below.
  • Velocity time constant: Time constant of 2.0 s, used in the speed control model, provides a smooth response.
  • Time delay: A pure delay associated with both the speed and path control algorithms. The value of 0.2 seconds is typical of values that have been derived from laboratory studies of manual control. This parameter is considered to represent a driver limitation rather than a preference.
  • Pedal transition time: The time to transition (s) between brake and throttle. On-road data suggest values in the range of 0.5 to 1 s. Because the DVM does not allow the driver to anticipate the need to switch pedals, however, a negligible value of one integration time interval has been used for analysis with the DVM.
  • Preview time constant: A parameter which, when multiplied by the effective time constant of the path-control loop, determines the amount of preview associated with reacting to road curvature. Model analysis indicates that a value of about 0.8 s provides good lateral tracking in a curve.
  • Wait-stop time: The time (s) required for the vehicle to remain at a stop sign before proceeding. The value of 3 s was arbitrarily selected. (A nonzero value is required to ensure that the vehicle will come to a complete stop and then proceed.)
  • Acceleration and braking gains: Parameters of the speed control algorithm. Values shown were adjusted to provide smooth and responsive speed response for the passenger car model. Different values will generally be needed for other vehicle models and can be determined through analysis of the models contained in VDANL.
  • Acceleration and braking time constants: Additional parameters (s) of the speed control algorithm. Adjusted as described for the associated gain parameters.
  • Maximum sight distance: This SD (m) represents SD limitations imposed by factors other than highway geometry, such as weather conditions and limitations on the driver's ability to see at night. The value of 1,000 m is appropriate to daytime conditions and is considered large enough to have no impact on driver speed decision.

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.

Table 8. Parameter values for two driver types.
Driver Type Free Speed (km/h) Lateral Acceleration Factor Preferred Longitudinal Acceleration (g)
Average 105 36.0 0.048
85th Percentile 114 41.3 .068

Free Speed

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:

Equation 42. X subscript 85 equals M plus Z subscript 85 times sd (42)

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:

Mean: 28.6

Maximum: 34.8

Minimum: 23.6

sd 3.1

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:

  1. Driver behavior corresponding to three horizontal curves explored in the Battelle on-road study were selected for analysis because (a) they required clear reductions in speed, (b) speed behavior in each curve was felt to be dominated by own-curve characteristics, and (c) at least 9 subjects provided reliable data. The parameters of these curves are shown in Table 9 .
  2. K was estimated from each value of implied lateral acceleration through an inversion of equation 41.
  3. The standard deviation of K was computed for each curve.
  4. The three standard deviations were averaged to provide an overall estimate of the standard deviation of K, and the calculation of equation 42 was used to compute the estimated 85th percentile value for K. The mean estimate of 36.0 obtained from visually fitting the acceleration data was used in this calculation.
Table 9. Parameters of curves selected for estimating statistics of the lateral acceleration factor.
Curve No. Geom. Radius (m) Virtual Radius (m) Virtual Curvature (rad/m) Virtual Curvature (deg/100 ft)
3 125 136 0.0074 12.8
5 146 154 0.0065 11.3
6 125 130 0.0077 13.4

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:

Equation 43. ax subscript o equals 0.245 times Delta V to the one half power. (43)

where

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:

Mean: 0.47

Maximum: 0.92

Minimum: 0.20

sd 0.14

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

Background

Parameters related to vehicle dynamic response and driver performance limitations were quantified. Parameters remaining to be determined were:

  • Guidelines for curve cutting.
  • The free speed which drivers adopt on sufficiently long stretches of tangent segments where neither the geometry of the road ahead, traffic, nor posted speed limits are factors in determining vehicle speed.
  • The lateral acceleration factor, which defines the relationship between curvature, speed, and lateral acceleration in a horizontal curve.
  • The maximum lateral acceleration that the driver willingly tolerates in a horizontal curve.
  • The nominal longitudinal acceleration-the preferred acceleration when either speeding up or slowing down.
  • The maximum longitudinal acceleration that the driver will employ when braking beyond the preferred level is necessary. (The DVM is not intended to be applied to true emergency situations in which the driver applies maximum force to the brake pedal.)

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:

  • Level tangent sections with the highest speed limits allowed, without traffic, and sufficiently long so that preceding and succeeding horizontal geometry would not affect the asymptotic speed.
  • Horizontal curves of varying radii separated by long tangent sections so that the influence of a specific radius of curvature could be determined free of confounding by other geometric features.
  • Portions of the study in which the drivers were instructed to brake at the maximum comfortable level, and negotiate curves at the maximum comfortable level.

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.

Test Route

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. Line graph. X/Y plot of test route. The graph shows the comparison of the plan views to the test route.

Figure 14. X/Y plot of test route.

Figure 15. Line graph. Vertical profile, with test route and analytic route almost identical.

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.

On-road Data

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.

Table 10. Replications of on-road data used for model analysis.
Driver No. Rep. 1 Rep. 2 Rep. 3 Rep. 4
1 x x x x
2 x x x x
3   x x  
5 x x x  

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. Line graph. Mean first and last speed profile. The graph shows a close correspondence between the mean of the four drivers of the first run, and the mean of the four drivers of the last run.

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. Line graph. Road curvature. The graph indicates magnitude of curvature in radians per meter versus station in meters.

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. Line graph. Mean speed profile for four drivers. The graph indicates speed in meters per second versus station in meters.

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.

Calibration/Validation Methods

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.

Results

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.

Table 11. Summary of validation results for the heavy vehicle.
Driver-related Parameters Validation Results
Curve cutting The outer right rear trailer wheels tracked outside the right lane boundary when negotiating the 100-m curve in both runs and came very close to the lane boundary in the 200-m curve when cutting the curve.The driver was able to cut the 300-m curve without the rear wheels crossing the lane boundary, but for the curve deflection explored here, there were negligible changes in predicted speed and predicted lateral acceleration compared to maintaining lane center. The user is advised to assume for the purposes of model analysis that the driver of a tractor-trailer type of heavy vehicle attempts to maintain lane center in the absence of lane widening at the site of the curve. (At present, the model does not accommodate the assumption that the driver attempts to track to the outside in a curve.)The model parameter always keep center should be set to TRUE.
Nominal longitudinal acceleration The longitudinal acceleration and deceleration preferred by the automobile driver depends on the total change in speed. An analytic expression relating acceleration or deceleration to the magnitude of the resulting speed change reproduces the trends of the on-road data.Because the steady-state (cruising) speeds on short tangents connecting horizontal curves is expected to be less than the free speed that might be obtained on very long tangents, the preferred acceleration will generally depend on the length of the tangent and the speeds appropriate to negotiating the adjacent curves. At present, the model does not predict cruising speeds in such situations, and the user must specify a preferred acceleration that is representative of the highway environment. For the model analysis described here, a representative value of 0.032 g was selected from visual inspection of the longitudinal acceleration profiles observed in the on-road data.
Lateral acceleration factor For the most part, the predicted speed is determined by the posted speed limits and not by the horizontal geometry.A comparison of the predicted speed profile to the vertical road profile suggests that speed was reduced in the region of station 2000 because of acceleration limits of the heavy vehicle. Inspection of the predicted accelerator profile reveals maximum pedal deflection during the period when the predicted vehicle falls below the prevailing miles per hour speed limit.Reducing the lateral acceleration factor to 20 yielded a predicted speed profile that was within one standard deviation of the experimental mean profile for almost the entire distance, as shown in figure 20.
Horizontal sight distance limitations Selecting the full stop option (the driver assumes that an obstruction requiring a full stop lies just beyond the sight distance) for testing sight distance limitations degraded the overall match to the measured speed profile. Predicted speed variations were greater than in the previous analyses, with the speed dropping well below one standard deviation from the mean at two locations. Further study is required to determine how horizontal sight distance limitations influence driver behavior and how to model such effects.

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.

Table 12. Parameters related to driver preference.
Parameter Function Car Truck
Preview time constant (s) Path control 0.8 1.0
Gain margin 3.0 3.0
Speed time constant (s) Speed control 2.0 2.0
Acceleration gain 0.1 0.1
Braking gain 1.0 0.5
Able to cut curve? Path decision T F(1)
Lane margin (m) 0.3 NA
Free speed (km/h) Speed decision 105 105(2)
Lateral acceleration factor 36 20
Maximum lateral acceleration (g) 0.4(3) 0.4(3)
Nominal longitudinal acceleration (g) PD(4) PD(4)
Maximum longitudinal acceleration (g) 0.2(3) 0.2(3)

Notes:

  1. In general, it is not advantageous for the truck driver to track to the inside of the curve. More likely the driver will track to the outside of the curve to minimize the likelihood of the trailer crossing the lane boundaries-a behavior not currently handled by the DVM.
  2. Data were not available for determining this parameter for the heavy vehicle. The value associated with passenger car is suggested pending further study.
  3. Based on engineering assumptions in the absence of data available to calibrate this parameter.
  4. Problem dependent. Values of 0.048 g and 0.032 g were found to characterize the data available for passenger car and heavy vehicle drivers, respectively. These values may be more reflective of speed limit restrictions than differences between car and truck drivers.

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:

  • Improvement to the tire rolling drag portion of VDANL.
  • Implementation of engine braking systems and retarders.
  • Improvement of the model's ability to start on an upgrade or a downgrade.
  • Update of the thermal brake model with a newer, enhanced version of the model.
  • Implementation of the bump stop model.
  • Implementation of the model for damper and bump stop track widths for solid axles.
  • Implementation of the ability to change tire characteristics based on roadway surface condition.
  • Addition of the capability to model multi-axle vehicles and trailers.

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United States Department of Transportation - Federal Highway Administration