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Length-based vehicle classification using event-based loop detector data
Transportation Research Part C 38 (2014) 156–166
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Length-based vehicle classification using event-based loop detector data Henry X. Liu ⇑, Jie Sun Department of Civil Engineering, University of Minnesota, 500 Pillsbury Drive S.E., Minneapolis, MN 55455, United States
a r t i c l e
i n f o
Article history: Received 6 August 2013 Received in revised form 7 November 2013 Accepted 7 November 2013
Keywords: Vehicle classification Vehicle length Inductive loop detector Event-based loop detector data Car-following model
a b s t r a c t Length-based vehicle classification is an important topic in traffic engineering, because estimation of traffic speed from single loop detectors usually requires the knowledge of vehicle length. In this paper, we present an algorithm that can classify vehicles passing by a loop detector into two categories: long vehicles and regular cars. The proposed algorithm takes advantage of event-based loop detector data that contains every vehicle detector actuation and de-actuation ‘‘event’’, therefore time gaps between consecutive vehicles and detector occupation time for each vehicle can be easily derived. The proposed algorithm is based on an intuitive observation that, for a vehicle platoon, longer vehicles in the platoon will have relatively longer detector occupation time. Therefore, we can identify longer vehicles by examining the changes of occupation time in a vehicle platoon. The method was tested using the event-based data collected from Trunk Highway 55 in Minnesota, which is a high speed arterial corridor controlled by semi-actuated coordinated traffic signals. The result shows that the proposed method can correctly classify most of the vehicles passing by a single loop detector. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Single inductive loop detectors (ILDs) have been widely deployed in almost all the metropolitan areas in the United States. Traditionally, if aggregated detector occupancy and volume measurements (e.g. in 30 s interval) are available, then space mean traffic speed at the detector location can be estimated by using these measurements together with a manually-calibrated effective vehicle length. It is also well-known that the error of the estimated speed is linearly proportional to the error of the effective vehicle length, which is dependent on vehicle composition that may vary at different locations and different times. Therefore, frequent calibration of effective vehicle length is usually required to ensure the accuracy of speed estimation. Such effort is usually time-consuming and costly. Although it is possible to get vehicle class information via technologies such as weigh in motion (WIM) station, piezo sensors, video imaging, or acoustic signal analysis (Jolly et al., 1996; Nooralahiyan et al., 1997; Avery et al., 2004), none of these technologies, however, are as widely deployed as ILDs. With the widespread deployment of ILDs, there will be no or little extra installation cost if ILDs can be used for vehicle classification. ILDs can be configured in the form of single loop detector or dual loop detectors. Dual loop detectors consist of two single inductive loop detectors placed closely together and such setting allows direct estimation of vehicle speed and length, which enables length-based vehicle classification (Nihan et al., 2002; Cheevarunothai et al., 2007). However, the deployment of dual detectors is also limited compared with that of single loop detectors.
⇑ Corresponding author. Tel.: +1 612 625 6347. E-mail addresses: [email protected] (H.X. Liu), [email protected] (J. Sun). 0968-090X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.trc.2013.11.010
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A number of researchers also investigated length-based vehicle classification using vehicle signature from ILDs (Oh et al., 2002; Cheung et al., 2005; Jeng and Ritchie, 2008; Jeng et al., 2013). Vehicles can be classified into more than 3 classes and the reported accuracy can be higher than 80%. However, in order to generate vehicle signature from ILDs, special data acquisition card with high scan rate is required, which limits its deployment because of cost. Researchers have also used aggregated data (e.g. with 30 s interval) from single loop detector for vehicle classification (Kwon et al., 2003; Wang and Nihan, 2003, 2004). Kwon et al. (2003) developed a vehicle classification algorithm based on speed correlation between lanes. With assumed existence of a truck-free lane, the speed of that lane can be estimated using the measured volume and occupancy data from a single loop detector. The estimated speed for the truck-free lane can then be used to derive the effective vehicle length for other lanes based on speed correlation. Wang and Nihan (2003, 2004) classified vehicles by separating time intervals (20 s in their case) with long vehicles from those without in a time period (5 min in their case), and by assuming constant speed within the time period. Then they used the speed estimated from those car-only intervals, in which vehicle length was known, to derive effective vehicle length and vehicle composition for those intervals with long vehicles. Both approaches described above, however, rely on the assumption that a benchmark, either a truck-free lane or a truck-free time interval, is available so that traffic speed can be estimated using known length of regular cars. It is apparent that such assumptions can be easily violated. Coifman and Kim (2009) is the only exception that uses the event-based data from a single loop detector to identify vehicle length. The event-based loop detector data contains every vehicle detector actuation and de-actuation ‘‘event’’, therefore time gaps between consecutive vehicles and detector occupation time for each vehicle can be easily derived. They studied the probability distribution of the detector occupation time (i.e., the detector on-time actuated by individual vehicles), and classify a vehicle by associating its detector actuation time with that distribution. Since low vehicle speed also creates high actuation time, their method performs poorly during congestion, as reported in their paper. In contrast to the statistical based method used by Coifman and Kim (2009), a method based on traffic flow theory is proposed in this paper. The proposed algorithm is based on an intuitive observation that, for a vehicle platoon, longer vehicles in the platoon will have relatively longer detector occupation time. Using event-based data, we first group vehicles into platoons according to the time gaps between vehicles. We then use Newell’s simplified car-following theory (Newell, 2002) to describe the relation between consecutive vehicles in a platoon. Observed vehicle occupation time is compared with estimated vehicle occupation time. Discrepancy between these two is used to identify long vehicles by comparing the ratio between them with predefined critical length ratio. The proposed method is tested using event-based traffic data collected from Trunk Highway 55 in Minnesota and concurrently recorded videos are used for verification. This paper is organized as follows. The event-based traffic data are briefly explained and some initial observations from the field data are offered in Section 2. In Section 3, the speed relation between consecutive vehicles is described by applying Newell’s simplified car-following model, and a vehicle classification algorithm is developed by comparing the measured occupation time with the estimated occupation time of each vehicle in Section 4. Field test results are shown in the Section 5 and concluding remarks are offered in Section 6. 2. Data description and empirical observation 2.1. Event-based data collection The event-based data was collected by using the SMART-Signal system developed by the University of Minnesota (Liu and Ma, 2009; Liu et al., 2009). In the SMART-Signal system, every vehicle-detector actuation and every signal phase change are recognized and recorded as an event. From event-based data, time gap between two consecutive vehicles can be easily calculated by using the time difference between two detector actuation events, and detector occupation time is simply the time difference between a detector actuation event and its following de-actuation event. In this paper, field data was collected from the intersection of Trunk Highway 55 (TH-55) and Glenwood Ave. by using the SMART-Signal system (see Fig. 1). Detector 3 is used to collect the event-based data. This is an advanced detector located at 400 feet upstream of the stop line. The outer lane is purposefully chosen, as more long vehicles are expected to travel in outer lane. Data from a typical weekday (on June 3, 2008) are used. Concurrent video was recorded for verification purpose. 2.2. Field observation The motion of a vehicle traveling in a platoon closely following the vehicle in its front can be approximately described by a car-following model. Assuming the vehicles in a platoon have the same acceleration rate (a) when passing by a fixed location, the traffic flow can be in one of three categories based on the value of a. If a = 0, we call it steady flow; if a > 0, acceleration flow; if a < 0, deceleration flow. As the inductive loop detector gives point measurement of the traffic flow, it is convenient to see how the speeds change when vehicles passing by a detector. In steady flow, acceleration flow and deceleration flow, the speed of vehicles in the
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Fig. 1. Study site.
traffic keeps about the same, increasing, or decreasing, respectively, when passing by a detector. Free flow traffic is an example of steady flow. Discharging flow when signal turns to green can be seen as an example of acceleration flow. And deceleration flow can be observed where vehicles arrive at an intersection when the signal is red. Despite of different traffic flow patterns, a spike in terms of individual vehicle occupation time can always be observed in event-based data when a long vehicle passes by a detector. Figs. 2–4 show the detector occupation times in three different traffic signal cycles with the presence of long vehicles in steady flow, acceleration flow, and deceleration flow, respectively. The x-axes are colored according to the signal statuses at that time. 2.2.1. Steady flow Fig. 2 shows an example of a spike in vehicle occupation time in steady flow traffic. The traffic was not congested and the signal status at the intersection was green during the time of interest. So the traffic is in steady flow. Based on the analysis above, the observed spike in occupation time indicates a long vehicle. And using video recorded concurrently, it is confirmed that there was a long vehicle (big truck) passing by at that time. 2.2.2. Acceleration flow When traffic accelerates (for example at the start of green), individual vehicle occupation times are supposed to become smaller and smaller, as vehicles accelerate. Even if there are fluctuations in speed and differences in vehicle lengths, the occupation time is unlikely to have a dramatic change. Therefore if a dramatic change is observed with detector occupation
Fig. 2. Detector occupation time spike caused by long vehicle (steady traffic flow).
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Fig. 3. Detector occupation time spike caused by long vehicle (acceleration traffic flow).
Fig. 4. Detector occupation time spike caused by long vehicle (deceleration traffic flow).
time, it indicates a long vehicle in the traffic. An example can be seen in Fig. 3, where the traffic accelerated at the start of green time. The result was verified against video. 2.2.3. Deceleration flow When traffic decelerates, the speeds of consecutive vehicles passing by a detector are expected to decrease gradually. In this situation, an occupation time spike still suggests a long vehicle. Fig. 4 demonstrates the occupation time spike caused by a long vehicle in deceleration flow, where occupation times increase gradually because of red light. The observation is also verified by video. 2.3. Analysis The goal of this study is to identify long vehicles (LVs) in traffic. Vehicles, whose lengths are at least as 2 or 3 times as that of a regular car (RC), are regarded as long vehicles in this study. Although long vehicles cause occupation time spike in all traffic conditions, the problem is to quantitatively determine the criteria for long vehicle identification. Recall that occupation time (o) equals to effective vehicle length (l) divided by vehicle speed (v), i.e. o = l/v. Single vehicle occupation time is affected by both vehicle length and vehicle speed. On the other hand, inductive loop detectors only give measurements of occupation time. For an individual vehicle, it is impossible to tell its vehicle length without knowing its speed or vice versa. However, the speeds of vehicles in a platoon are closely related. If the speed relation
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between consecutive vehicles can be quantitatively described, the relative length between consecutive vehicles can also be estimated, although it is still difficult to calculate the absolute vehicle length. Given most vehicles on road are not long vehicles (Kwon et al., 2003; Wang and Nihan, 2003), long vehicles can be identified by utilizing relative vehicle lengths. 3. Theoretical foundations of vehicle classification 3.1. Newell’s simplified car following model and its extension Newell (2002) proposed a simplified car-following model, in which the trajectory of a vehicle is approximately the same as its leading vehicle with a displacement in space d and in time s (see Fig. 5). Eq. (1) describes the trajectories of two consecutive vehicles according to Newell’s car-following model. Here xn1 is the location of leading vehicle and xn is the location of following vehicle. dn and sn are assumed to be related to the driving behavior of the following vehicle’s driver.
xn ðt þ sn Þ ¼ xn1 ðtÞ dn
ð1Þ
Assume that the acceleration rate of the leading vehicle n 1 is a. Then, the trajectory of the leading vehicle can be described by Eq. (2), where a is the speed changing rate and vn1 is the initial speed.
xn1 ¼
a 2 t þ v n1 t 2
ð2Þ
Consequently, the trajectory of the following vehicle can be described by Eq. (3), which is derived from Eqs. (1) and (2). Newell’s assumption implies that the speed changing rate of the following vehicle is the same as that of the leading vehicle.
xn ¼
a ðt sn Þ2 þ v n1 ðt sn Þ dn 2
ð3Þ
Assume the leading vehicle passes by the detector at time zero, then the location of the detector will be zero as well (setting t to be zero in Eq. (2)). Denote the speed of leading vehicle when it passes by the detector by vn1, and the speed of following vehicle when it passes by the detector by vn. When the following vehicle passes by the detector, xn equals to zero in Eq. (3), as the detector locates at zero. Then solve for t and only keep the positive solution, since the vehicles are moving forward. The solution is
t ¼
ðv n1 asn Þ þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v 2n1 þ 2adn
ð4Þ
a
The speed of the following vehicle n, when it passes by the detector, can be calculated by differentiating Eq. (3) with respect to t and plugging in Eq. (4), which would be
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
v n ¼ v 2n1 þ 2adn
ð5Þ
Fig. 5. Newell’s simplified car-following model.
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3.2. Estimation of vehicle occupation time In traffic flow, a vehicle can be either (1) far away from its immediate front vehicle, or (2) following its immediate front vehicle. In the first situation, the vehicle travels at its desired speed (all the vehicles are assumed to have the same desired speed in this study). In the second situation, the trajectory of the vehicle can be described by Newell’s car-following model discussed in Section 3.1. Event-based traffic data include individual vehicle occupation time (detector on-time) and the gap between consecutive vehicles. Assuming that a vehicle is not following its immediate leading vehicle if the gap between them is greater than or equal to a critical gap n, then a sequence of vehicles can be divided into multiple groups based on the gaps between consecutive vehicles using n. The gaps between vehicles within a group are all smaller than n. Vehicles in different groups are not following each other. Vehicles within a group are following the immediate front vehicle in the group and thus their trajectories can be described by Newell’s car-following model. Let n denotes the number of vehicles in a group. If n < 2, the vehicles are assumed to travel at desired speed. If n = 2, the 1st vehicle is assumed to travel at free flow speed. Given its measured occupation time, its effective vehicle length can be calculated. The effective vehicle length of the 2nd vehicle can be estimated by comparing its occupation time to that of the 1st vehicle. When n P 3, estimated speed of each vehicle within a group is calculated by Eq. (5), given the speed of the first vehicle v0, the acceleration rate a, and the space displacement dn. The space displacement of vehicle trajectory d is the property of a vehicle or a driver and direct measurement of d is difficult. For practical application, calibration may be needed. For research purpose in this study, the value of d is estimated to be 24 feet based on the results of other researches (Ahn et al., 2004; Chiabaut et al., 2009; Wang and Coifman, 2005). With space displacement d fixed, the speed of vehicles within a group is a function of the leading vehicle speed v0 and acceleration rate a. Assuming all the vehicles are not long vehicles and their effective lengths are l, the estimated occupation time for ith vehicle is
^i ¼ o
l
ð6Þ
v^ i
^ i is the estimated speed of ith vehicle and can be calculated by Eq. (5). where v The mean square error (MSE) vehicle occupation time is calculated as,
^ ¼1 MSEð0Þ n
n X ^i oi Þ2 ðo
ð7Þ
i¼0
For the situation where n P 3 optimal
v0 and a is obtained from the following minimization program,
^Þ min MSEðo s:t:
10 ft=s2 < a < 7 ft=s2
ð8Þ
0 mph < v < 100 mph where a is the acceleration rate of vehicles and v is the speed of all the vehicles in the group. The constraints are added for the sake of both physical limit of vehicles and algorithm considerations. First, the acceleration rate and speeds of most vehicles will not go beyond the specified range. Second, when there is large change in occupation time, a curve with larger absolute acceleration rate value can usually fit data better. But this large change in occupation time is usually caused by long vehicles rather than unusual vehicle acceleration rate. With the estimated optimal v0 and a, estimated speed of each vehicle in a group is calculated using Eq. (5). Corresponding estimated occupation time is calculated by Eq. (6), assuming all vehicle effective lengths are l. 4. Vehicle classification algorithm As the proposed method applies on vehicle platoons, a pre-defined critical gap (n) is used to group the vehicles. In addition, the number of vehicles in a group is constrained to be less than a given number (nn), as it is found out the description of vehicle dynamics by car-following model becomes inaccurate, when the number of vehicles in a group is large. In case of n is greater than nn when grouping by gap data, this group of vehicles are further grouped by a moving window of nn vehicles. For example, if nn = 10 and we get a group of 12 vehicles by using gap data, then we have three sub groups, vehicle 1 to vehicle 10, vehicle 2 to vehicle 11, and vehicle 3 to vehicle 12. For vehicles appear in several subgroups, average estimated speed is used for classification procedure. The measured occupation time of each vehicle is compared with its estimated occupation time. If the ratio between these two is greater than or equal to a predefined critical ratio (d), this vehicle is classified as a long vehicle. A flowchart of vehicle classification algorithm is presented Fig. 6 and explanations are provided below.
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Algorithm V (vehicle classification) Data: Individual vehicle occupation time and gap. Result: A list of long vehicles. V1. [initialize to-be-processed] Each element in the list representing one vehicle with an occupation time and time gap. V2. [set processing list empty] processing list is a temporary list holding a group of vehicles to be classified. V3. [set processed list empty] processed list stores vehicle classification results. V4. [to-be-processed empty?] If yes, finish. V5. [add one vehicle to processing] move the first vehicle from to-be-processed to processing. V6. [make a group?] If current gap is greater than or equal to critical gap (n), or to-be-processed is empty, go to V7; otherwise, go to V4. V7. [size of processing > 3?] If yes go to V8; otherwise, go to V9. V8. [vehicle occupation time estimation using MSE minimization.] Get estimated vehicle occupation times using MSE minimization introduced at the end of Section 3. If the number of vehicles in a group is greater than nn, use moving sub groups method described at the end of first graph of this section. Then go to V10. V9. [simple method for vehicle occupation time estimation] Get estimated vehicle occupation time with desired speed and typical vehicle length. V10. [classification using critical occupation time ratio] For each vehicle, if the ratio between its measured occupation time and its estimated occupation time is greater than or equal to critical ratio, add it to long vehicle list. V11. [add classified vehicles to processed list and empty processing list] save results and go to V4.
A special treatment has to be made to the vehicles that have stopped or nearly stopped over the detectors. This can be usually observed at intersections with high traffic volume and when queues are built beyond the detector location. As inductive loop detector only gives vehicle occupation time, it is necessary to assume that vehicles with extremely large occupation time actually stopped over the detector. In this situation, little information about this vehicle can be extracted from the data. Since the majority of vehicles on the road are not long vehicles, these vehicles with extremely long occupation time are assumed not to be long vehicles. 5. Field test of the vehicle classification algorithm As we mentioned in Section 2, field data was collected from Detector 3 of the intersection of Trunk Highway 55 (TH-55) and Glenwood Ave. (Fig. 1) on June 3, 2008 between 6 and 9 am. During this period of time, 2547 sample data were collected. For verification purpose, concurrent video was also recorded. The outputs of the algorithm will be a list of long vehicles identified by the algorithm. The time when each long vehicle actuates the detector will also be output, which is verified against concurrently recorded video. The video is manually processed to identify the long vehicles passing by the detector during the test period. The desired speed of vehicles is assumed to be 50 mph or 73.3 ft/s (i.e., the free flow speed at the detector location based on archived data). The effective vehicle length of a regular car is estimated to be 24 feet based on the observation of field
Fig. 6. Vehicle classification algorithm flowchart.
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critical ratio = 1.5625
90
90
80
80
70
15
75
60 50 40 30 20
2438
4
16
2526
1
70 60 50 40 30 20
19
10 0
critical ratio = 2.4
100
estimated length (ft)
estimated length (ft)
100
10 0
20
40
60
80
100
observed length (ft)
0
0
20
40
60
80
100
observed length (ft)
Fig. 7. Field test results of the vehicle classification algorithm.
data. The choice of critical length ratio (d) is important. The lengths of vehicles on road are not uniformly distributed. For example, Wang and Nihan (2003) has shown that the distribution of vehicle lengths at a typical freeway location on I-5 is bi-normal distribution. The shorter vehicles had a mean length of 18 ft with a standard deviation of 3 ft and the long vehicles had a mean length of 73.8 ft with a standard deviation of 11.8 ft. If the critical length ratio is so chosen that it is larger than the value when shorter vehicles travel at slightly lower speed and smaller than the value when long vehicles travel at slightly higher speed, the algorithm will be more robust to the speed variation. Based on the published data (ASSHTO, 2004) and field observation, two critical length ratios are used. The first one (d1) is chosen to be 1.5625, which means vehicles with effective vehicle length equal to or longer than 37.5 ft (24 1.5625) are identified as long vehicles. The second critical length ratio is chosen to be 2.4, which means vehicles with effective vehicle length equal to or longer than 57.6 ft (24 2.4) are identified as long vehicles. As mentioned above, space displacement (d) is set to be 24 feet. Critical gap (n) is determined to be 8 s after calibration. Set nn = 10 after examining the data. The final results are given in Fig. 7. On the left is the test result when critical length ratio is 1.5625 and on the right is the test result when critical length ratio is 2.4. The numbers of correctly classified vehicles are shown in green and the numbers of incorrect classification are given in red. It can be observed that the long vehicle percentage is very low (around 3%), which agrees with general observation on TH-55. To evaluate an algorithm, it is necessary to have numerical measurements on its performance. Most of the time, it is adequate to use the accuracy, which is the total number of true results divided by the total number of samples. In our case, we are more interested in the long vehicles, but their occurrences are rare. The accuracy will be dominated by the results of regular cars. For example, one can achieve high accuracy by just setting all vehicles to be regular cars. To overcome this, more sophisticated measurements that focus on long vehicles (positive cases) are needed. As we have only two classes of vehicles, our algorithm can be regarded as binary classification, where two measurements, precision and recall, are usually used to evaluate the results. They can be calculated from the following coincidence matrix (see Table 1). Then precision and recall are calculated as:
precision ¼
recall ¼
TP TP þ FP
TP TP þ FN
Roughly speaking, precision can be interpreted as the probability of correctness when a positive prediction is made, and recall is the probability of correct identification when a true positive sample occurs. A more comprehensive measurement is F-measure (van Rijsbergen, 1979):
Table 1 A simple coincidence matrix (redrew from Olson and Dursun (2008, p. 138)). Predicted Class
Positive Negative
True Class Positive
Negative
True Positive Count (TP) False Negative Count (FN)
False Positive Count (FP) True Negative Count (TN)
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Table 2 Precision, recall and F-measure.
Critical length ratio = 1.5625 Critical length ratio = 2.4
F-measure ¼
TP
FP
FN
TN
Precision
Recall
F-measure
75 16
15 4
19 1
2438 2526
0.833333 0.8
0.797872 0.941176
0.815217 0.864865
2 1 þ recall
1 precision
F-measure, also known as F-score, is a weighted average of precision and recall, and reaches its best value at 1 and worst score at 0. Single numerical measurement makes it easier to compare multiple results. The precision, recall and F-measure of two field tests are given in Table 2. To put the performance of the proposed method into context, let’s apply a naïve method by assuming that all vehicles pass by the detector with free flow speed. The estimated effective vehicle lengths are calculated by multiplying measured occupation time with free flow speed. This method is usually used to calibrate effective vehicle length on freeways during mid of the day. Applying this naïve method to the 3 h test data, 38.74% of the vehicles will be identified as long vehicles if critical length ratio 1.5625 is used, and 18.21% of the vehicles will be identified as long vehicles if critical length ratio is set to 2.4. The recall value will be close to 1, as the almost all the long vehicles will be identified. But the precision is extremely low, which is about 0.08. Consequently, the F-measure of the naïve method is about 0.15, which is pretty low. The reason for the poor performance of the naïve method is that the assumption of free flow speed when vehicles pass by the detector no longer holds because of the interruption to traffic from traffic signals. Many vehicles pass by the detector with much lower speed or even stop over the detector when the signal is red or there is queue in front.
Fig. 8. Vehicle identification example 1.
Fig. 9. Vehicle identification example 2.
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In contrast, the proposed algorithm has much better performances. The F-measure is higher than 0.8 in both cases. By looking at the F-measure, the algorithm performed better when the critical length ratio is higher. This agrees with the intuition that it is easier to distinguish much longer vehicles from the regular cars. It is interesting to see what the data look like when the algorithm makes right identification and it will be even more interesting to look at the data when the algorithm gives incorrect results. Figs. 8 and 9 are both taken from the test when critical ratio is 1.5625, i.e. vehicles with effective lengths greater than or equal to 37.5 ft are considered as long vehicles. Fig. 8 shows the example when a long vehicle is correctly identified. The long vehicle caused an occupation time spike when the traffic slows down because of red light. Please refer to Fig. 4, where same data are used. The ratio between its measured and estimated occupation time is 1.657. This is greater than the critical length ratio 1.5625, so it is identified as a long vehicle and confirmed by the video observation. These are factors that are not considered in the proposed model, and in fact it might be difficult to consider all possible situations in a theoretical model. Fig. 9 shows one example of false positive and one example of true positive. The first occupation time spike is identified by the algorithm as a long vehicle, as its length ratio is 1.89. But from the video, it can be seen what really happened was that the vehicle at the left lane in front of the subject vehicle made a lane change and forced the subject vehicle slow down before it touched the detector. The second long vehicle identification is correct in this example. The occupation time spike was caused by a school bus. Although it traveled faster than it was supposed to, it is still identified as long vehicle. This is achieved by properly choosing the critical length ratio so that the algorithm is robust to small speed variations. 6. Conclusions In this paper, we propose an algorithm that can classify vehicles based on their lengths using event-based traffic data. The proposed algorithm is based on an intuitive observation that, for a vehicle platoon, longer vehicles in the platoon will cause irregularity in terms of detector occupation times. To exploiting the irregularity, it is necessary to describe the speed relation between vehicles. This is done by extending Newell’s simplified car-following model. The gap data from event-based traffic data are used to group vehicles traveling as a platoon, where it is appropriate to describe the speed relation by a car-following model. For each group of vehicles, a minimization program is used to find the best fitted initial speed and acceleration rate. Then by assuming all the vehicles have a typical length, an estimated occupation time is calculated for each vehicle. The estimated occupation time is compared with corresponding measured occupation time. These unusual high occupation times observed are regarded as indications of the presence of long vehicles. The proposed algorithm is readily applicable to event-based traffic data that is obtainable from single loop detectors, which have been widely deployed. The additional cost for implementation of such vehicle classification is expected to be low. Some calibration work may be necessary for the parameters used in the algorithm, but additional infrastructure cost is minimal. Although the test data were collected from signalized arterial, the proposed method should also be applicable for freeway loop detector data. A number of research directions can be explored based on the vehicle classification algorithm developed in this paper. One direct application of the proposed algorithm is to improve the speed estimation algorithm based on the loop detector data, as we discussed in the Introduction section of this paper. Another possible research direction is to leverage the proposed vehicle classification algorithm to improve the estimation accuracy of vehicle fuel consumption and pollution emission, which is important for the evaluation of environmental impacts of a new traffic control strategy. Acknowledgements The authors would like to thank Steve Misgen, Timothy Bangsund and Curt Krohn of the Minnesota Department of Transportation for their assistance in the field deployment of the research results on Trunk Highway 55 in Minnesota. Dr. Henry Liu and the University of Minnesota have equity and royalty interests in SMART Signal Technologies, Inc., a Minnesota-based private company which could commercially benefit from the results of this research. These relationships have been reviewed and managed by the University of Minnesota in accordance with its Conflict of Interests policies. References Ahn, S., Cassidy, M.J., Laval, J., 2004. Verification of a simplified car-following theory. Transportation Research Part B 38, 431–440. ASSHTO, 2004. A Policy on Geometric Design of Highways and Streets, fifth ed. American Association of Highway and Transportation. Avery, R.P., Wang, Y., Rutherford, G.S., 2004. Length-based vehicle classification using images from uncalibrated video cameras. In: Proceedings of the 7th International IEEE Conference on Intelligent Transportation Systems, pp. 737–742. Cheevarunothai, P., Wang, Y., Nihan, N.L., 2007. Using dual-loop event data to enhance truck data accuracy. Transportation Research Record: Journal of the Transportation Research Board 1993, 131–137. Cheung, S.Y., Coleri, S., Dundar, B., Ganesh, S., Tan, C.W., Varaiya, P., 2005. Traffic measurement and vehicle classification with single magnetic sensor. Transportation Research Record: Journal of the Transportation Research Board 1917, 173–181. Chiabaut, N., Buisson, C., Leclercq, L., 2009. Fundamental diagram estimation through passing rate measurements in congestion. IEEE Transactions on Intelligent Transportation Systems 10, 355–359.
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Coifman, B., Kim, S.B., 2009. Speed estimation and length based vehicle classification from freeway single-loop detectors. Transportation Research Part C 17, 349–364. Jeng, S.-T., Ritchie, S., 2008. Real-time vehicle classification using inductive loop signature data. Transportation Research Record: Journal of the Transportation Research Board 2086, 8–22. Jeng, S.-T. (Cindy), Chu, L., Hernadez, S.V., 2013. Vehicle Classification Approach Based on Wavelet K-Nearest Neighbor Using Inductive Loop Signatures. Presented at the 92nd Annual Meeting of the Transportation Research Board, Washington, DC. Jolly, M.P.D., Lakshmanan, S., Jain, A.K., 1996. Vehicle segmentation and classification using deformable templates. IEEE Transactions on Pattern Analysis and Machine Intelligence 18, 293–308. Kwon, J., Varaiya, P., Skabardonis, A., 2003. Estimation of truck traffic volume from single loop detectors with lane-to-lane speed correlation. Transportation Research Record: Journal of the Transportation Research Board 1856, 106–117. Liu, H.X., Ma, W., 2009. A virtual vehicle probe model for time-dependent travel time estimation on signalized arterials. Transportation Research Part C 17, 11–26. Liu, H.X., Wu, X., Ma, W., Hu, H., 2009. Real-time queue length estimation for congested signalized intersections. Transportation Research Part C 17, 412– 427. Newell, G.G., 2002. A simplified car-following theory: a lower order model. Transportation Research Part B 36, 195–205. Nihan, N.L., Zhang, X., Wang, Y., Briglia, P., 2002. Evaluation of Dual-Loop Data Accuracy Using Video Ground Truth Data. Transportation Northwest, Department of Civil Engineering, University of Washington. Nooralahiyan, A.Y., Dougherty, M., McKeown, D., Kirby, H.R., 1997. A field trial of acoustic signature analysis for vehicle classification. Transportation Research Part C 5, 165–177. Oh, S., Ritchie, S.G., Oh, C., 2002. Real-time traffic measurement from single loop inductive signatures. Transportation Research Record: Journal of the Transportation Research Board 1804, 98–106. Olson, D.L., Dursun, D., 2008. Advanced Data Mining Techniques, first ed. Springer. Van Rijsbergen, C.J. ‘‘Keith,’’ 1979. Information Retrieval, second ed. Butterworth, London, GB; Boston, MA. Wang, C., Coifman, B., 2005. The study on the effect of lane change maneuvers on a simplified car-following theory. IEEE Intelligent Transportation Systems. Proceedings, 478–483. Wang, Y., Nihan, N.L., 2003. Can single-loop detectors do the work of dual-loop detectors? Journal of Transportation Engineering 129, 169. Wang, Y., Nihan, N.L., 2004. Dynamic estimation of freeway large-truck volumes based on single-loop measurements. Journal of Intelligent Transportation Systems 8, 133–142.
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Transportation Research Part C journal homepage: www.elsevier.com/locate/trc
Length-based vehicle classification using event-based loop detector data Henry X. Liu ⇑, Jie Sun Department of Civil Engineering, University of Minnesota, 500 Pillsbury Drive S.E., Minneapolis, MN 55455, United States
a r t i c l e
i n f o
Article history: Received 6 August 2013 Received in revised form 7 November 2013 Accepted 7 November 2013
Keywords: Vehicle classification Vehicle length Inductive loop detector Event-based loop detector data Car-following model
a b s t r a c t Length-based vehicle classification is an important topic in traffic engineering, because estimation of traffic speed from single loop detectors usually requires the knowledge of vehicle length. In this paper, we present an algorithm that can classify vehicles passing by a loop detector into two categories: long vehicles and regular cars. The proposed algorithm takes advantage of event-based loop detector data that contains every vehicle detector actuation and de-actuation ‘‘event’’, therefore time gaps between consecutive vehicles and detector occupation time for each vehicle can be easily derived. The proposed algorithm is based on an intuitive observation that, for a vehicle platoon, longer vehicles in the platoon will have relatively longer detector occupation time. Therefore, we can identify longer vehicles by examining the changes of occupation time in a vehicle platoon. The method was tested using the event-based data collected from Trunk Highway 55 in Minnesota, which is a high speed arterial corridor controlled by semi-actuated coordinated traffic signals. The result shows that the proposed method can correctly classify most of the vehicles passing by a single loop detector. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Single inductive loop detectors (ILDs) have been widely deployed in almost all the metropolitan areas in the United States. Traditionally, if aggregated detector occupancy and volume measurements (e.g. in 30 s interval) are available, then space mean traffic speed at the detector location can be estimated by using these measurements together with a manually-calibrated effective vehicle length. It is also well-known that the error of the estimated speed is linearly proportional to the error of the effective vehicle length, which is dependent on vehicle composition that may vary at different locations and different times. Therefore, frequent calibration of effective vehicle length is usually required to ensure the accuracy of speed estimation. Such effort is usually time-consuming and costly. Although it is possible to get vehicle class information via technologies such as weigh in motion (WIM) station, piezo sensors, video imaging, or acoustic signal analysis (Jolly et al., 1996; Nooralahiyan et al., 1997; Avery et al., 2004), none of these technologies, however, are as widely deployed as ILDs. With the widespread deployment of ILDs, there will be no or little extra installation cost if ILDs can be used for vehicle classification. ILDs can be configured in the form of single loop detector or dual loop detectors. Dual loop detectors consist of two single inductive loop detectors placed closely together and such setting allows direct estimation of vehicle speed and length, which enables length-based vehicle classification (Nihan et al., 2002; Cheevarunothai et al., 2007). However, the deployment of dual detectors is also limited compared with that of single loop detectors.
⇑ Corresponding author. Tel.: +1 612 625 6347. E-mail addresses: [email protected] (H.X. Liu), [email protected] (J. Sun). 0968-090X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.trc.2013.11.010
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A number of researchers also investigated length-based vehicle classification using vehicle signature from ILDs (Oh et al., 2002; Cheung et al., 2005; Jeng and Ritchie, 2008; Jeng et al., 2013). Vehicles can be classified into more than 3 classes and the reported accuracy can be higher than 80%. However, in order to generate vehicle signature from ILDs, special data acquisition card with high scan rate is required, which limits its deployment because of cost. Researchers have also used aggregated data (e.g. with 30 s interval) from single loop detector for vehicle classification (Kwon et al., 2003; Wang and Nihan, 2003, 2004). Kwon et al. (2003) developed a vehicle classification algorithm based on speed correlation between lanes. With assumed existence of a truck-free lane, the speed of that lane can be estimated using the measured volume and occupancy data from a single loop detector. The estimated speed for the truck-free lane can then be used to derive the effective vehicle length for other lanes based on speed correlation. Wang and Nihan (2003, 2004) classified vehicles by separating time intervals (20 s in their case) with long vehicles from those without in a time period (5 min in their case), and by assuming constant speed within the time period. Then they used the speed estimated from those car-only intervals, in which vehicle length was known, to derive effective vehicle length and vehicle composition for those intervals with long vehicles. Both approaches described above, however, rely on the assumption that a benchmark, either a truck-free lane or a truck-free time interval, is available so that traffic speed can be estimated using known length of regular cars. It is apparent that such assumptions can be easily violated. Coifman and Kim (2009) is the only exception that uses the event-based data from a single loop detector to identify vehicle length. The event-based loop detector data contains every vehicle detector actuation and de-actuation ‘‘event’’, therefore time gaps between consecutive vehicles and detector occupation time for each vehicle can be easily derived. They studied the probability distribution of the detector occupation time (i.e., the detector on-time actuated by individual vehicles), and classify a vehicle by associating its detector actuation time with that distribution. Since low vehicle speed also creates high actuation time, their method performs poorly during congestion, as reported in their paper. In contrast to the statistical based method used by Coifman and Kim (2009), a method based on traffic flow theory is proposed in this paper. The proposed algorithm is based on an intuitive observation that, for a vehicle platoon, longer vehicles in the platoon will have relatively longer detector occupation time. Using event-based data, we first group vehicles into platoons according to the time gaps between vehicles. We then use Newell’s simplified car-following theory (Newell, 2002) to describe the relation between consecutive vehicles in a platoon. Observed vehicle occupation time is compared with estimated vehicle occupation time. Discrepancy between these two is used to identify long vehicles by comparing the ratio between them with predefined critical length ratio. The proposed method is tested using event-based traffic data collected from Trunk Highway 55 in Minnesota and concurrently recorded videos are used for verification. This paper is organized as follows. The event-based traffic data are briefly explained and some initial observations from the field data are offered in Section 2. In Section 3, the speed relation between consecutive vehicles is described by applying Newell’s simplified car-following model, and a vehicle classification algorithm is developed by comparing the measured occupation time with the estimated occupation time of each vehicle in Section 4. Field test results are shown in the Section 5 and concluding remarks are offered in Section 6. 2. Data description and empirical observation 2.1. Event-based data collection The event-based data was collected by using the SMART-Signal system developed by the University of Minnesota (Liu and Ma, 2009; Liu et al., 2009). In the SMART-Signal system, every vehicle-detector actuation and every signal phase change are recognized and recorded as an event. From event-based data, time gap between two consecutive vehicles can be easily calculated by using the time difference between two detector actuation events, and detector occupation time is simply the time difference between a detector actuation event and its following de-actuation event. In this paper, field data was collected from the intersection of Trunk Highway 55 (TH-55) and Glenwood Ave. by using the SMART-Signal system (see Fig. 1). Detector 3 is used to collect the event-based data. This is an advanced detector located at 400 feet upstream of the stop line. The outer lane is purposefully chosen, as more long vehicles are expected to travel in outer lane. Data from a typical weekday (on June 3, 2008) are used. Concurrent video was recorded for verification purpose. 2.2. Field observation The motion of a vehicle traveling in a platoon closely following the vehicle in its front can be approximately described by a car-following model. Assuming the vehicles in a platoon have the same acceleration rate (a) when passing by a fixed location, the traffic flow can be in one of three categories based on the value of a. If a = 0, we call it steady flow; if a > 0, acceleration flow; if a < 0, deceleration flow. As the inductive loop detector gives point measurement of the traffic flow, it is convenient to see how the speeds change when vehicles passing by a detector. In steady flow, acceleration flow and deceleration flow, the speed of vehicles in the
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Fig. 1. Study site.
traffic keeps about the same, increasing, or decreasing, respectively, when passing by a detector. Free flow traffic is an example of steady flow. Discharging flow when signal turns to green can be seen as an example of acceleration flow. And deceleration flow can be observed where vehicles arrive at an intersection when the signal is red. Despite of different traffic flow patterns, a spike in terms of individual vehicle occupation time can always be observed in event-based data when a long vehicle passes by a detector. Figs. 2–4 show the detector occupation times in three different traffic signal cycles with the presence of long vehicles in steady flow, acceleration flow, and deceleration flow, respectively. The x-axes are colored according to the signal statuses at that time. 2.2.1. Steady flow Fig. 2 shows an example of a spike in vehicle occupation time in steady flow traffic. The traffic was not congested and the signal status at the intersection was green during the time of interest. So the traffic is in steady flow. Based on the analysis above, the observed spike in occupation time indicates a long vehicle. And using video recorded concurrently, it is confirmed that there was a long vehicle (big truck) passing by at that time. 2.2.2. Acceleration flow When traffic accelerates (for example at the start of green), individual vehicle occupation times are supposed to become smaller and smaller, as vehicles accelerate. Even if there are fluctuations in speed and differences in vehicle lengths, the occupation time is unlikely to have a dramatic change. Therefore if a dramatic change is observed with detector occupation
Fig. 2. Detector occupation time spike caused by long vehicle (steady traffic flow).
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Fig. 3. Detector occupation time spike caused by long vehicle (acceleration traffic flow).
Fig. 4. Detector occupation time spike caused by long vehicle (deceleration traffic flow).
time, it indicates a long vehicle in the traffic. An example can be seen in Fig. 3, where the traffic accelerated at the start of green time. The result was verified against video. 2.2.3. Deceleration flow When traffic decelerates, the speeds of consecutive vehicles passing by a detector are expected to decrease gradually. In this situation, an occupation time spike still suggests a long vehicle. Fig. 4 demonstrates the occupation time spike caused by a long vehicle in deceleration flow, where occupation times increase gradually because of red light. The observation is also verified by video. 2.3. Analysis The goal of this study is to identify long vehicles (LVs) in traffic. Vehicles, whose lengths are at least as 2 or 3 times as that of a regular car (RC), are regarded as long vehicles in this study. Although long vehicles cause occupation time spike in all traffic conditions, the problem is to quantitatively determine the criteria for long vehicle identification. Recall that occupation time (o) equals to effective vehicle length (l) divided by vehicle speed (v), i.e. o = l/v. Single vehicle occupation time is affected by both vehicle length and vehicle speed. On the other hand, inductive loop detectors only give measurements of occupation time. For an individual vehicle, it is impossible to tell its vehicle length without knowing its speed or vice versa. However, the speeds of vehicles in a platoon are closely related. If the speed relation
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between consecutive vehicles can be quantitatively described, the relative length between consecutive vehicles can also be estimated, although it is still difficult to calculate the absolute vehicle length. Given most vehicles on road are not long vehicles (Kwon et al., 2003; Wang and Nihan, 2003), long vehicles can be identified by utilizing relative vehicle lengths. 3. Theoretical foundations of vehicle classification 3.1. Newell’s simplified car following model and its extension Newell (2002) proposed a simplified car-following model, in which the trajectory of a vehicle is approximately the same as its leading vehicle with a displacement in space d and in time s (see Fig. 5). Eq. (1) describes the trajectories of two consecutive vehicles according to Newell’s car-following model. Here xn1 is the location of leading vehicle and xn is the location of following vehicle. dn and sn are assumed to be related to the driving behavior of the following vehicle’s driver.
xn ðt þ sn Þ ¼ xn1 ðtÞ dn
ð1Þ
Assume that the acceleration rate of the leading vehicle n 1 is a. Then, the trajectory of the leading vehicle can be described by Eq. (2), where a is the speed changing rate and vn1 is the initial speed.
xn1 ¼
a 2 t þ v n1 t 2
ð2Þ
Consequently, the trajectory of the following vehicle can be described by Eq. (3), which is derived from Eqs. (1) and (2). Newell’s assumption implies that the speed changing rate of the following vehicle is the same as that of the leading vehicle.
xn ¼
a ðt sn Þ2 þ v n1 ðt sn Þ dn 2
ð3Þ
Assume the leading vehicle passes by the detector at time zero, then the location of the detector will be zero as well (setting t to be zero in Eq. (2)). Denote the speed of leading vehicle when it passes by the detector by vn1, and the speed of following vehicle when it passes by the detector by vn. When the following vehicle passes by the detector, xn equals to zero in Eq. (3), as the detector locates at zero. Then solve for t and only keep the positive solution, since the vehicles are moving forward. The solution is
t ¼
ðv n1 asn Þ þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v 2n1 þ 2adn
ð4Þ
a
The speed of the following vehicle n, when it passes by the detector, can be calculated by differentiating Eq. (3) with respect to t and plugging in Eq. (4), which would be
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
v n ¼ v 2n1 þ 2adn
ð5Þ
Fig. 5. Newell’s simplified car-following model.
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3.2. Estimation of vehicle occupation time In traffic flow, a vehicle can be either (1) far away from its immediate front vehicle, or (2) following its immediate front vehicle. In the first situation, the vehicle travels at its desired speed (all the vehicles are assumed to have the same desired speed in this study). In the second situation, the trajectory of the vehicle can be described by Newell’s car-following model discussed in Section 3.1. Event-based traffic data include individual vehicle occupation time (detector on-time) and the gap between consecutive vehicles. Assuming that a vehicle is not following its immediate leading vehicle if the gap between them is greater than or equal to a critical gap n, then a sequence of vehicles can be divided into multiple groups based on the gaps between consecutive vehicles using n. The gaps between vehicles within a group are all smaller than n. Vehicles in different groups are not following each other. Vehicles within a group are following the immediate front vehicle in the group and thus their trajectories can be described by Newell’s car-following model. Let n denotes the number of vehicles in a group. If n < 2, the vehicles are assumed to travel at desired speed. If n = 2, the 1st vehicle is assumed to travel at free flow speed. Given its measured occupation time, its effective vehicle length can be calculated. The effective vehicle length of the 2nd vehicle can be estimated by comparing its occupation time to that of the 1st vehicle. When n P 3, estimated speed of each vehicle within a group is calculated by Eq. (5), given the speed of the first vehicle v0, the acceleration rate a, and the space displacement dn. The space displacement of vehicle trajectory d is the property of a vehicle or a driver and direct measurement of d is difficult. For practical application, calibration may be needed. For research purpose in this study, the value of d is estimated to be 24 feet based on the results of other researches (Ahn et al., 2004; Chiabaut et al., 2009; Wang and Coifman, 2005). With space displacement d fixed, the speed of vehicles within a group is a function of the leading vehicle speed v0 and acceleration rate a. Assuming all the vehicles are not long vehicles and their effective lengths are l, the estimated occupation time for ith vehicle is
^i ¼ o
l
ð6Þ
v^ i
^ i is the estimated speed of ith vehicle and can be calculated by Eq. (5). where v The mean square error (MSE) vehicle occupation time is calculated as,
^ ¼1 MSEð0Þ n
n X ^i oi Þ2 ðo
ð7Þ
i¼0
For the situation where n P 3 optimal
v0 and a is obtained from the following minimization program,
^Þ min MSEðo s:t:
10 ft=s2 < a < 7 ft=s2
ð8Þ
0 mph < v < 100 mph where a is the acceleration rate of vehicles and v is the speed of all the vehicles in the group. The constraints are added for the sake of both physical limit of vehicles and algorithm considerations. First, the acceleration rate and speeds of most vehicles will not go beyond the specified range. Second, when there is large change in occupation time, a curve with larger absolute acceleration rate value can usually fit data better. But this large change in occupation time is usually caused by long vehicles rather than unusual vehicle acceleration rate. With the estimated optimal v0 and a, estimated speed of each vehicle in a group is calculated using Eq. (5). Corresponding estimated occupation time is calculated by Eq. (6), assuming all vehicle effective lengths are l. 4. Vehicle classification algorithm As the proposed method applies on vehicle platoons, a pre-defined critical gap (n) is used to group the vehicles. In addition, the number of vehicles in a group is constrained to be less than a given number (nn), as it is found out the description of vehicle dynamics by car-following model becomes inaccurate, when the number of vehicles in a group is large. In case of n is greater than nn when grouping by gap data, this group of vehicles are further grouped by a moving window of nn vehicles. For example, if nn = 10 and we get a group of 12 vehicles by using gap data, then we have three sub groups, vehicle 1 to vehicle 10, vehicle 2 to vehicle 11, and vehicle 3 to vehicle 12. For vehicles appear in several subgroups, average estimated speed is used for classification procedure. The measured occupation time of each vehicle is compared with its estimated occupation time. If the ratio between these two is greater than or equal to a predefined critical ratio (d), this vehicle is classified as a long vehicle. A flowchart of vehicle classification algorithm is presented Fig. 6 and explanations are provided below.
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Algorithm V (vehicle classification) Data: Individual vehicle occupation time and gap. Result: A list of long vehicles. V1. [initialize to-be-processed] Each element in the list representing one vehicle with an occupation time and time gap. V2. [set processing list empty] processing list is a temporary list holding a group of vehicles to be classified. V3. [set processed list empty] processed list stores vehicle classification results. V4. [to-be-processed empty?] If yes, finish. V5. [add one vehicle to processing] move the first vehicle from to-be-processed to processing. V6. [make a group?] If current gap is greater than or equal to critical gap (n), or to-be-processed is empty, go to V7; otherwise, go to V4. V7. [size of processing > 3?] If yes go to V8; otherwise, go to V9. V8. [vehicle occupation time estimation using MSE minimization.] Get estimated vehicle occupation times using MSE minimization introduced at the end of Section 3. If the number of vehicles in a group is greater than nn, use moving sub groups method described at the end of first graph of this section. Then go to V10. V9. [simple method for vehicle occupation time estimation] Get estimated vehicle occupation time with desired speed and typical vehicle length. V10. [classification using critical occupation time ratio] For each vehicle, if the ratio between its measured occupation time and its estimated occupation time is greater than or equal to critical ratio, add it to long vehicle list. V11. [add classified vehicles to processed list and empty processing list] save results and go to V4.
A special treatment has to be made to the vehicles that have stopped or nearly stopped over the detectors. This can be usually observed at intersections with high traffic volume and when queues are built beyond the detector location. As inductive loop detector only gives vehicle occupation time, it is necessary to assume that vehicles with extremely large occupation time actually stopped over the detector. In this situation, little information about this vehicle can be extracted from the data. Since the majority of vehicles on the road are not long vehicles, these vehicles with extremely long occupation time are assumed not to be long vehicles. 5. Field test of the vehicle classification algorithm As we mentioned in Section 2, field data was collected from Detector 3 of the intersection of Trunk Highway 55 (TH-55) and Glenwood Ave. (Fig. 1) on June 3, 2008 between 6 and 9 am. During this period of time, 2547 sample data were collected. For verification purpose, concurrent video was also recorded. The outputs of the algorithm will be a list of long vehicles identified by the algorithm. The time when each long vehicle actuates the detector will also be output, which is verified against concurrently recorded video. The video is manually processed to identify the long vehicles passing by the detector during the test period. The desired speed of vehicles is assumed to be 50 mph or 73.3 ft/s (i.e., the free flow speed at the detector location based on archived data). The effective vehicle length of a regular car is estimated to be 24 feet based on the observation of field
Fig. 6. Vehicle classification algorithm flowchart.
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critical ratio = 1.5625
90
90
80
80
70
15
75
60 50 40 30 20
2438
4
16
2526
1
70 60 50 40 30 20
19
10 0
critical ratio = 2.4
100
estimated length (ft)
estimated length (ft)
100
10 0
20
40
60
80
100
observed length (ft)
0
0
20
40
60
80
100
observed length (ft)
Fig. 7. Field test results of the vehicle classification algorithm.
data. The choice of critical length ratio (d) is important. The lengths of vehicles on road are not uniformly distributed. For example, Wang and Nihan (2003) has shown that the distribution of vehicle lengths at a typical freeway location on I-5 is bi-normal distribution. The shorter vehicles had a mean length of 18 ft with a standard deviation of 3 ft and the long vehicles had a mean length of 73.8 ft with a standard deviation of 11.8 ft. If the critical length ratio is so chosen that it is larger than the value when shorter vehicles travel at slightly lower speed and smaller than the value when long vehicles travel at slightly higher speed, the algorithm will be more robust to the speed variation. Based on the published data (ASSHTO, 2004) and field observation, two critical length ratios are used. The first one (d1) is chosen to be 1.5625, which means vehicles with effective vehicle length equal to or longer than 37.5 ft (24 1.5625) are identified as long vehicles. The second critical length ratio is chosen to be 2.4, which means vehicles with effective vehicle length equal to or longer than 57.6 ft (24 2.4) are identified as long vehicles. As mentioned above, space displacement (d) is set to be 24 feet. Critical gap (n) is determined to be 8 s after calibration. Set nn = 10 after examining the data. The final results are given in Fig. 7. On the left is the test result when critical length ratio is 1.5625 and on the right is the test result when critical length ratio is 2.4. The numbers of correctly classified vehicles are shown in green and the numbers of incorrect classification are given in red. It can be observed that the long vehicle percentage is very low (around 3%), which agrees with general observation on TH-55. To evaluate an algorithm, it is necessary to have numerical measurements on its performance. Most of the time, it is adequate to use the accuracy, which is the total number of true results divided by the total number of samples. In our case, we are more interested in the long vehicles, but their occurrences are rare. The accuracy will be dominated by the results of regular cars. For example, one can achieve high accuracy by just setting all vehicles to be regular cars. To overcome this, more sophisticated measurements that focus on long vehicles (positive cases) are needed. As we have only two classes of vehicles, our algorithm can be regarded as binary classification, where two measurements, precision and recall, are usually used to evaluate the results. They can be calculated from the following coincidence matrix (see Table 1). Then precision and recall are calculated as:
precision ¼
recall ¼
TP TP þ FP
TP TP þ FN
Roughly speaking, precision can be interpreted as the probability of correctness when a positive prediction is made, and recall is the probability of correct identification when a true positive sample occurs. A more comprehensive measurement is F-measure (van Rijsbergen, 1979):
Table 1 A simple coincidence matrix (redrew from Olson and Dursun (2008, p. 138)). Predicted Class
Positive Negative
True Class Positive
Negative
True Positive Count (TP) False Negative Count (FN)
False Positive Count (FP) True Negative Count (TN)
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Table 2 Precision, recall and F-measure.
Critical length ratio = 1.5625 Critical length ratio = 2.4
F-measure ¼
TP
FP
FN
TN
Precision
Recall
F-measure
75 16
15 4
19 1
2438 2526
0.833333 0.8
0.797872 0.941176
0.815217 0.864865
2 1 þ recall
1 precision
F-measure, also known as F-score, is a weighted average of precision and recall, and reaches its best value at 1 and worst score at 0. Single numerical measurement makes it easier to compare multiple results. The precision, recall and F-measure of two field tests are given in Table 2. To put the performance of the proposed method into context, let’s apply a naïve method by assuming that all vehicles pass by the detector with free flow speed. The estimated effective vehicle lengths are calculated by multiplying measured occupation time with free flow speed. This method is usually used to calibrate effective vehicle length on freeways during mid of the day. Applying this naïve method to the 3 h test data, 38.74% of the vehicles will be identified as long vehicles if critical length ratio 1.5625 is used, and 18.21% of the vehicles will be identified as long vehicles if critical length ratio is set to 2.4. The recall value will be close to 1, as the almost all the long vehicles will be identified. But the precision is extremely low, which is about 0.08. Consequently, the F-measure of the naïve method is about 0.15, which is pretty low. The reason for the poor performance of the naïve method is that the assumption of free flow speed when vehicles pass by the detector no longer holds because of the interruption to traffic from traffic signals. Many vehicles pass by the detector with much lower speed or even stop over the detector when the signal is red or there is queue in front.
Fig. 8. Vehicle identification example 1.
Fig. 9. Vehicle identification example 2.
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In contrast, the proposed algorithm has much better performances. The F-measure is higher than 0.8 in both cases. By looking at the F-measure, the algorithm performed better when the critical length ratio is higher. This agrees with the intuition that it is easier to distinguish much longer vehicles from the regular cars. It is interesting to see what the data look like when the algorithm makes right identification and it will be even more interesting to look at the data when the algorithm gives incorrect results. Figs. 8 and 9 are both taken from the test when critical ratio is 1.5625, i.e. vehicles with effective lengths greater than or equal to 37.5 ft are considered as long vehicles. Fig. 8 shows the example when a long vehicle is correctly identified. The long vehicle caused an occupation time spike when the traffic slows down because of red light. Please refer to Fig. 4, where same data are used. The ratio between its measured and estimated occupation time is 1.657. This is greater than the critical length ratio 1.5625, so it is identified as a long vehicle and confirmed by the video observation. These are factors that are not considered in the proposed model, and in fact it might be difficult to consider all possible situations in a theoretical model. Fig. 9 shows one example of false positive and one example of true positive. The first occupation time spike is identified by the algorithm as a long vehicle, as its length ratio is 1.89. But from the video, it can be seen what really happened was that the vehicle at the left lane in front of the subject vehicle made a lane change and forced the subject vehicle slow down before it touched the detector. The second long vehicle identification is correct in this example. The occupation time spike was caused by a school bus. Although it traveled faster than it was supposed to, it is still identified as long vehicle. This is achieved by properly choosing the critical length ratio so that the algorithm is robust to small speed variations. 6. Conclusions In this paper, we propose an algorithm that can classify vehicles based on their lengths using event-based traffic data. The proposed algorithm is based on an intuitive observation that, for a vehicle platoon, longer vehicles in the platoon will cause irregularity in terms of detector occupation times. To exploiting the irregularity, it is necessary to describe the speed relation between vehicles. This is done by extending Newell’s simplified car-following model. The gap data from event-based traffic data are used to group vehicles traveling as a platoon, where it is appropriate to describe the speed relation by a car-following model. For each group of vehicles, a minimization program is used to find the best fitted initial speed and acceleration rate. Then by assuming all the vehicles have a typical length, an estimated occupation time is calculated for each vehicle. The estimated occupation time is compared with corresponding measured occupation time. These unusual high occupation times observed are regarded as indications of the presence of long vehicles. The proposed algorithm is readily applicable to event-based traffic data that is obtainable from single loop detectors, which have been widely deployed. The additional cost for implementation of such vehicle classification is expected to be low. Some calibration work may be necessary for the parameters used in the algorithm, but additional infrastructure cost is minimal. Although the test data were collected from signalized arterial, the proposed method should also be applicable for freeway loop detector data. A number of research directions can be explored based on the vehicle classification algorithm developed in this paper. One direct application of the proposed algorithm is to improve the speed estimation algorithm based on the loop detector data, as we discussed in the Introduction section of this paper. Another possible research direction is to leverage the proposed vehicle classification algorithm to improve the estimation accuracy of vehicle fuel consumption and pollution emission, which is important for the evaluation of environmental impacts of a new traffic control strategy. Acknowledgements The authors would like to thank Steve Misgen, Timothy Bangsund and Curt Krohn of the Minnesota Department of Transportation for their assistance in the field deployment of the research results on Trunk Highway 55 in Minnesota. Dr. Henry Liu and the University of Minnesota have equity and royalty interests in SMART Signal Technologies, Inc., a Minnesota-based private company which could commercially benefit from the results of this research. 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