EXPLORING VARIATION IN DETECTION ERRORS OF WIRELESS MAGNETOMETERS AND SPAN WIRE CAMERAS USING CONDITIONAL INFERENCE TREES. (TRB Paper No.

Transcription

1 EXPLORING VARIATION IN DETECTION ERRORS OF WIRELESS MAGNETOMETERS AND SPAN WIRE CAMERAS USING CONDITIONAL INFERENCE TREES (TRB Paper No ) Jidong Yang, Ph.D., P.E. (Corresponding Author) Assistant Professor Department of Civil and Construction Engineering Kennesaw State University 00 South Marietta Parkway Marietta, GA Phone : (678) , jyang2@kennesaw.edu Sung-Hee Kim, Ph.D., P.E. Associate Professor Department of Civil and Construction Engineering Kennesaw State University 00 South Marietta Parkway Marietta, GA Phone: (678) , skim86@kennesaw.edu Bashan Zuo Research Assistant Kennesaw State University 00 South Marietta Parkway Marietta, GA Phone: (678) , bzuo@students.kennesaw.edu Submitted for Presentation at the 206 TRB Annual Meeting and Publication in the Journal of the Transportation Research Board Word Count: 7,300 (3,050 words for text, 2 figures, and 5 tables) Revised: November 6,

2 ABSTRACT In the paper, two stop bar vehicle detection technologies, wireless magnetometers and span wire cameras, are evaluated. Those technologies are considered to be practically suitable for large intersections, where span wire is generally required to achieve longer spans. To explore potential factors underlying variation in detection errors of those technologies, conditional inference trees were employed. The results indicated that the wireless magnetometers are quite robust to various weather and environmental conditions if there is reliable communication between in-pavement magnetometers and the repeater and/or access point. The addition of a repeater at the study site significantly reduced false and stuck-on call errors potentially caused by the frequent passing of heavy trucks. In contrast, the span wire camera is more susceptible to various weather and environmental conditions, and wind appears to be an influential factor, especially for false call errors. Keywords: detection error, wireless magnetometer, span wire camera, conditional inference tree 2

3 INTRODUCTION Vehicle detection technologies have been rapidly evolved over the past decade due to the advancement of sensors and wireless communication technologies and increasing deployment of traffic-responsive and adaptive traffic control systems, which heavily rely on robust vehicle detection. The traditional inductive-loop detector was introduced in the early 960s and since then has become the dominating vehicle sensor in modern traffic signal control systems. With a long history of deployment, inductive-loop detectors have exposed many problems. They are susceptible to pavement cracking, labor intensive for maintenance over time, and cause traffic disruption for repair. Additionally, resurfacing of roadways or utility repairs may require reinstallation of these types of sensors. Because of those practical concerns, less intrusive or nonintrusive vehicle detection technologies have emerged. However, at large intersections, which typically require span wire for signal support, vehicle detection options are rather limited besides the inductive loop. Among those, wireless magnetometers is one of such options that has been widely used in the U.S. With no need for cabling from the cabinet to the in-pavement sensors, it is much easier to install and maintain, and cause less disruption to traffic for installation and repair as compared to inductive loops. Given the much smaller size, they are less likely to malfunction due to pavement deterioration. Unlike inductive loops, wireless magnetometers can be reused when the pavement is resurfaced. In addition, the directional sensors can reduce the false calls from vehicles traveling in different directions. However, because it uses the unlicensed frequency band (2400 to MHz) for communication between the in-pavement sensors and an access point or a repeater, disruption might occur due to various reasons. Also, latency might be an issue depending on the field condition and setup. Previous studies (-4) of this technology has been focused on its application for vehicle counting. More recently, studies have been shifted to evaluating it as a vehicle detector at signalized intersections (5, 6). In this context, Day et al. conducted a study focusing on the latency and recommended optimal spacing of magnetometers to minimize missed calls (5). Medina et al. evaluated the performance of wireless magnetometers under adverse weather conditions by simple comparison (6). On the other hand, span wire cameras are recently emerged to allow for mounting of the camera on span wires. This new technology has a potential to greatly expand the application of cameras for vehicle detection at large signalized intersections. In this paper, both technologies, i.e., wireless magnetometers and span wire cameras, were evaluated at the intersection of South Marietta Parkway and Technology Parkway in the City of Marietta, Georgia, shown in Figure. 3

4 FIGURE Illustration of the test site. Regardless of practical drawbacks, inductive loops have been recognized as the most accurate and reliable vehicle detectors if they are functioning and thus were used as the benchmark or ground truth for evaluating the two technologies, wireless magnetometers and span wire cameras, in this study. TEST SITE SETUP At the time of the field study, the City of Marietta was in a process of replacing all inductive loops with wireless magnetometers at the intersection. Therefore, both inductive loops and wireless magnetometers were present during the study periods. This technology transition from inductive loops to wireless magnetometers at this location allows the research team to install three new wireless magnetometers (at 5 feet apart) in the northbound left turn lane within the confine of the existing loop (40 feet by 6 feet) as illustrated in Figure. In this setting, the inductive loop was used as a benchmark to evaluate the wireless magnetometers. For the span wire camera, it would be preferred to install the camera to detect the same northbound left turn lane as the wireless magnetometers. However, this northbound approach is susceptible to 4

5 view blocking due to frequent passing of heavy trucks. This phenomenon can be clearly seen in Figure FIGURE 2 Northbound approach view blocking due to frequent passing of heavy trucks on South Marietta Parkway. Because of this blocking issue, the span wire camera was installed to detect the westbound left turn movement, which has dual left turn lanes. The existing inductive loops (Figure ) for the westbound left turn movement were used as the benchmark to evaluate the span wire camera. It should be noted that frequent heavy trucks often move slowly and are sometimes stalled in the middle of the intersection due to extended queues at the downstream intersection of South Marietta Parkway and Cobb Parkway during peak periods of traffic. This extended blocking by trucks likely interrupts the communication between the wireless magnetometers and the antenna mounted on the strain pole at the northeast corner of the intersection. In fact, some large stuck-on calls were captured during peak hours of the initial test period. In light of this issue, a repeater was later added to the strain pole at the southwest corner to improve communication. The aerial view of the field setup for the wireless magnetometers and the span wire camera are illustrated in Figure 3. 5

6 Yang, Kim and Zuo Span Wire Camera Existing Antenn New Repeater Cabinet Magnetometers FIGURE 3 Field setup of wireless magnetometers and span wire camera. DATA DESCRIPTION Detection errors have generally been defined as discrepancies from the true condition. Four types of detection errors were commonly referenced: missed call, false call, stuck-on call, and dropped calls. Similar definition by Medina et al. (7) was adopted in this study by referencing the inductive loop as a benchmark. As such, the detection error is defined as a discrepancy between the test device (span wire camera or wireless magnetometers) and the inductive loop conditional upon the immediate prior state of detection, as shown in Table. These discrepancies are illustrated in Figure 4. TABLE Definition of Erroneous Calls (Detection Errors) Status Change 40 Missed Call Test Loop Device Type of Erroneous Calls False Call Stuck-on Call Test Test Loop Loop Device Device Before (t -) After 0 0 (t +) Notes: 0 = detector status is on; = detector status if off. 6 Dropped Call Test Loop Device 0 0

7 Figure 4 Illustration of detection error types. As seen, a missed call is defined as the loop detector registered a call (status =) while the test device did not (status =0), implying a vehicle is present at the stop bar but was not detected by the test device. A dropped call is defined as the test device erroneously released a previously registered call (status change from to 0) while the call is still held by the loop detector (status = ), implying a vehicle is still present at the stop bar but was erroneously dropped by the test device. A false call is defined as the test device registered a call but the loop detector did not, implying a wrong call was placed by the test device. A stuck-on call is defined as the loop detector has released a previously registered call while the call is still being held by the test device, meaning the vehicle has departed from the stop bar but the call is still erroneously held by the test device. Given the cyclic error patterns corresponding to the signal cycle, the average error per cycle for each type of erroneous calls was computed and used as performance indicator. Concurrent weather information for the test periods were extracted from the closest weather station through the weather underground website (wunderground.com), including wind speed, visibility, and various weather events. Weather events experienced at the test site during the test periods are presented in Table 2. 7

8 63 TABLE 2 Field Test Periods and Weather Information Test Device Wireless Magnetometer without the repeater with the repeater Span Wire Camera Period of Field Test From 2/3/205 0:0:28 AM 3//205 :9:43 PM 3//205 :9:58 PM To 2/20/205 3/20/205 3/20/205 :3:08 PM :5:05 PM :5:8 PM Clear Y Y Y Partly Cloudy Y Y Y Scattered Clouds Y Y Y Mostly Cloudy Y Y Y Overcast Y Y Y Light rain or drizzle Y Y Y Mist n/a Y Y Fog n/a Y Y Haze n/a Y Y Light Snow Y n/a n/a Notes: Y Indicates presence of the weather event. n/a not applicable. Weather Event For analysis purposes, similar weather events were grouped together and assigned an ordinal number by referencing clear weather as baseline. A higher number indicates more severe weather event. The coding for various weather events and other variable is presented in Table 3. TABLE 3. Variables and Data Coding Variable Description Unit/Value Wind Speed Wspeed Actual wind speed mile per hour (mph) Clear 0 Cloudy or overcast Weather Event Cond Light rain or drizzle 2 Mist, fog, or haze 3 Light snow 4 Lighting Night Day or Night 0 = Day; = Night Visibility Level Visibility Distance mile Repeater RP A repeater was added 0 = without repeater = with repeater 8

9 DATA ANALYSIS The descriptive statistics of variables considered are summarized in Table 4. TABLE 4 Summary of Descriptive Statistics Wireless Magnetometers Variable Unit Freq Mean SD Median Min Max Wspeed mph 5, Visibility mile 5, ,927 Weather 2 65 Group N 3,493 Night Y,736 N 2,82 RP Y 3,047 Span Wire Camera Variable Unit Freq Mean SD Median Min Max Wspeed mph 3, Visibility mile 3, Weather Group Night 0 9 3, N 2,384 Y,524 The video recorded through the span wire camera was reviewed. Example images illustrating detection status of the span wire camera under various conditions are shown in Figure 5. It can be seen that wind and reflection due to wet pavement cause detection errors. 9

10 Yang, Kim and Zuo FIGURE 5 Detection by the span wire camera under various conditions. Besides visual examination, the temporal change of detection errors was plotted along with concurrent weather and environmental conditions. Upon reviewing those plots, it is rather difficult to visually detect any patterns except that a sudden reduction of false and stuck-on calls is evident for the wireless magnetometers after a repeater had been added. This can be clearly seen in Figure 6. In order to identify factors or conditions underlying variation in detection errors of the test devices, regression trees were constructed for different error types and are discussed in the following section. 0

11 97 98 a) False Calls b) Stuck-on Calls FIGURE 6 Evident reduction of detection errors (false and stuck-on calls) for wireless magnetometers after installation of a repeater.

12 CONDITIONAL INFERENCE TREES Recursive partitioning is a fundamental tool in data mining. It helps explore the structure of data, while developing easy-to-visualize decision rules for predicting a categorical (classification tree) or continuous (regression tree) outcome. The conditional distribution of statistics measuring the association between responses and covariates is the basis for unbiased selection among covariates measured at different scales (8). In this study, conditional inference trees (ctree) in the R party package (9) was used to construct regression trees to reveal associations between detection errors (responses) and potential influential factors or conditions (covariates). Details on the methodology of conditional inference trees have been described by Hothorn et al. (8). A brief discussion of the conditional inference trees is provided below for reference. By assuming that the conditional distribution D(Y X) of the response variable Y given the covariates X depends on a function of X, f(x). The covariate space is partitioned into finite disjoint cells using the regression relationship to be fitted based on a learning sample. To determine whether there is any information about the response variable covered by any of the m covariates, a global hypothesis test is used. Given m covariates, the global hypothesis of independence is formulated in terms of the m partial hypotheses as, where :,,,. When H0 cannot be rejected at a pre-specified level, the recursion stops. If the global hypothesis is rejected, the association between Y and each of the covariates Xj is measured by test statistics or P-values indicating the deviation from the partial hypotheses. Specifically, a generic algorithm that recursively partition a sample is formulated using non-negative integer valued case weights. Each node of a tree is represented by a vector of case weights, which have non-zero elements when the corresponding observations are elements of the node and are zero otherwise. The algorithm involves two steps: ) variable selection, and 2) splitting. In step, the covariate of strongest association with the response (i.e., with the minimum p value) is selected for splitting. In step 2, a permutation test framework (0) is used to find the optimal binary split for the selected covariate in step. The goodness of a split is evaluated by a two-sample linear statistic that measures the discrepancy between the samples. The two steps are repeated recursively until the global null hypothesis of independence between the response and any of the covariates cannot be rejected at a pre-specified level, say Bonferroni-adjusted p- value was used in this case. As a result, conditional inference trees for wireless magnetometers were constructed for the false call error and stuck-on call error, as shown in Figures 7 and 8. For the missed call error and dropped call error, no trees can be established based on the variable selection and splitting criteria. 2

13 243 RP p < n = 282 y = FIGURE 7 Wireless magnetometer (false calls). As shown in Figure 7, y indicates the mean detection error in millisecond and n indicates the number of observations for each leaf or branch. As a result, the only significant factor to explain the variance of false call errors for wireless magnetometers is whether the repeater is added. As seen, the addition of the repeater significantly reduces the false call error from an average of milliseconds to milliseconds. RP p < n = 3047 y = Cond p < Cond p = n = 947 y = n = 235 y = n = 267 y = n = 430 y = FIGURE 8 Wireless magnetometers (stuck-on calls). Similarly, Figure 8 shows that the addition of the repeater results in drastic reduction in stuck-on call error. The repeater appears to mitigate the impact of adverse weather conditions (Cond >). The largest stuck-on call error ( milliseconds) occurred under more adverse weather conditions (Cond > ) when there was no repeater. The smallest stuck-on call error (.997 milliseconds) occurred under more favorable weather conditions (Cond ) after the repeater had been installed. For the span wire camera, conditional inference trees were constructed for all missed, false, stuckon, and dropped call errors and are shown in Figures

14 FIGURE 9 Span wire camera (missed calls). As shown in Figure 9, the largest missed call error (mean = 4.33 milliseconds) occurred during the day when the wind speed is between 4.6 mph and 3.8 mph. But, stronger wind (speed greater than 3.8 mph) is somehow associated with smaller missed call errors (0.595 milliseconds). This might be due to the algorithm compensating for higher wind speeds. The smallest missed call error occurred during the day when the wind speed is less than 4.6 mph and the visibility is less than 7 mph. At the night, larger missed call errors occurred under more severe weather conditions (Cond>2) FIGURE 0 Span wire camera (false calls). 4

15 As indicated in Figure 0, the largest false call error occurred when the wind speed is less than 5.8 mph, under more adverse weather conditions (Cond >), and with a higher visibility (greater than 7 mph). In general, night and adverse weather conditions (Cond > ) tend to increase the false call error. Night p < Wspeed p < n = 524 y = Cond p < n = 76 y = n = 574 y = n = 94 y = FIGURE Span wire camera (stuck-on calls). As shown in Figure, the largest stuck-on call error (420.8 milliseconds) occurred during the day when the wind speed is equal to or less than 5.8 mph and under more adverse weather conditions (Cond > ). The smallest stuck-on call error ( milliseconds) occurred at the night FIGURE 2 Span wire camera (dropped calls). 5

16 As indicated in Figure 2, the largest dropped call error occurred during the day when the visibility is less than 2 miles and the wind speed is greater than 5.8 mph. The night condition appears to be associated with larger dropped call errors. Increased visibility (greater than 2 miles) likely reduces the dropped call error. A higher wind speed (greater than 5.8 mph) tends to increase the dropped call error as well. In summary, the directions of error association with different factors or conditions are presented in Table 5. Factor TABLE 5 Summary of Conditional Inference Tree Analysis Missed Wireless Magnetometers False Dropped Missed False Span Wire Camera Stuckon Stuckon Dropped Night Weather Visibility Wind speed +/ Repeater - - Note: +, positive association -, negative association +/-, mixed depending on other factors. As seen in Table 5, the wireless magnetometers are quite robust to various weather and environmental conditions except that adverse weather likely increases the stuck-on call. But, the addition of a repeater at the study site has greatly reduced both stuck-on and false call errors. This implies that robust communication between the in-pavement sensors and the repeater and access point is critical for accurate and reliable detection for wireless magnetometers. On the other hand, the span wire camera is generally more sensitive to various weather, wind, visibility, and lighting conditions. More adverse weather events tend to increase the missed, false and stuck-on call errors. Night condition was associated with larger false and dropped call errors but smaller missed and stuck-on call errors. Better visibility appears to be associated with larger missed and false call errors, but smaller dropped call errors. Higher wind speed tends to increase dropped call errors. 6

17 CONCLUSION Technologies for replacing inductive loops at large intersections with the span wire support is rather limited. Wireless magnetometers and span wire cameras are two such technologies. Wireless magnetometers have been widely deployed in the U.S. On the other hand, span wire cameras are recently emerged and currently experimented by many agencies. Based on the results of this study, the wireless magnetometers appear to be quite robust to various weather and environmental conditions if they are set up properly and communication between in-pavement magnetometers and the repeaters/access point is reliable. Potential signal blocking by large trucks should be considered during field setup. In comparison, the span wire camera is more susceptible to various weather and environmental conditions. It requires good lane marking as reference for automatic adjustment during windy situation. Still wind appears to be an influential factor, especially for false call errors. The large errors under certain conditions indicate that this technology may require further refinement for improved accuracy and reliability. ACKNOWLEDGEMENTS This work is part of a research project sponsored by the Georgia Department of Transportation. The study was conducted with the Sensys wireless magnetometer detection unit and the Iteris Vantage SmartSpan detection unit. REFERENCES. Cheung, S. Y., S. Coleri, B. Dundar, S. Ganesh, C.-W. Tan, and P. Varaiya. Traffic Measurement and Vehicle Classification with Single Magnetic Sensor. In Transportation Research Record: Journal of the Transportation Research Board, No. 97, Transportation Research Board of the National Academies, Washington, D.C., 2005, pp Haoui, A., R. Kavaler, and P. Varaiya. Wireless Magnetic Sensors for Traffic Surveillance. Transportation Research Part C, Vol. 6, 2008, pp Margulici, J. D., S. Yang, and C.-W. Tan. Evaluation of Wireless Traffic Sensors by Sensys Networks, Inc. California Department of Transportation, Sacramento, Cheung, S.-Y., and P. Varaiya. Traffic Surveillance by Wireless Sensor Networks: Final Report. UCB-ITS-PRR University of California, Berkeley, Christopher M. Day, Hiromal Premachandra, Thomas M. Brennan, Jr., James R. Sturdevant, and Darcy M. Bullock. Operational Evaluation of Wireless Magnetometer Vehicle Detectors at Signalized Intersection. Journal of the Transportation Research Board, No. 292, Transportation Research Board of the National Academies, Washington, D.C., 200, pp Juan C. Medina, Rahim F. Benekohal, and Ali Hajbabaie. Evaluation of Sensys Wireless Vehicle Detection System: Results from Adverse Weather Conditions. Research Report ICT- -8, Illinois Center for Transportation, March Juan C. Medina, Madhav Chitturi, Rahim F. Benekohal. Illumination and Wind Effects on Video Detection Performance at Signalized Intersections, TRB 2008 Annual Meeting CD- ROM. 8. Hothorn T, Hornik K, Zeileis A (2006). Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics, 5 (3),

18 R Core Team (204). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 0. Strasser H and Weber C (999). On the Asymptotic Theory of Permutation Statistics. Mathematical Methods of Statistics, 8,