Taylor, Muthiah, Kulakowski, Mahoney an Porter 1 AN ARTIFICIAL NEURAL NETWORK SPEED PROFILE MODEL FOR HIGH- SPEED HIGHWAY CONSTRUCTION WORK ZONES Submission Date: August 1, 2005 Wor Count: 57 wors DOUGLAS R. TAYLOR Xerox Corporation Mail Stop 0207-01Z 800 Phillips Roa Webster, NY 14580 Tel:585-2-8188 DouglasR.Taylor@xerox.com (e-mail) SARAVANAN MUTHIAH Grauate Stuent (Pennsylvania State University) Room 114-B, Builing B, Pennsylvania Transportation Institute, University Park, PA 16802. Tel:814-8-6162 osm100@psu.eu (e-mail) BOHDAN T. KULAKOWSKI - Corresponing Author Professor of Mechanical Engineering (Pennsylvania State University) 201, Pennsylvania Transportation Institute, University Park, PA 16802. Tel:814-863-1893 btk1@psu.eu (e-mail) KEVIN M. MAHONEY Senior Research Associate The Pennsylvania State University Pennsylvania Transportation Institute 201 Transportation Research Builing University Park, PA 16802-4710 Tel: (814) 8-2815 Fax: (814) 8-3039 kmm28@psu.eu (e-mail) Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 2 R. J. PORTER Research Assistant The Pennsylvania State University Pennsylvania Transportation Institute 201 Transportation Research Builing University Park, PA 16802-4710 Tel: (814) 8-2814 Fax: (814) 8-3039 rjp167@psu.eu (e-mail) Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 3 ABSTRACT Spee profile moels can be use by highway engineers to assess the aequacy of a esign. Previous work has investigate relationships between operating spee an geometric roaway elements for permanent roaway conitions, mostly two-lane rural roas. No research of this type has been one for construction work zones. For this reason, a spee profile moel for high-spee highway construction work zones was successfully evelope using artificial neural networks (ANN) an implemente into an EXCEL spreasheet. The moel inputs inclue geometric features of the roa as well as variables specific to construction work zones. The output of the moel is a spee versus istance plot for cars, trucks an all vehicles. Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 4 INTRODUCTION One of the most complex issues relate to roaway esign is vehicle operating spee. This issue is even further complicate in construction work zones ue to spee reuction from pre-project conitions an transitions into the work zone. Construction work zones also typically contain aitional esign features such as temporary traffic barriers, reuce lane withs, an crossover sections that may influence vehicle spee. The Manual on Uniform Traffic Control Devices (MUTCD) states, [a] Temporary Traffic Control (TTC) plan shoul be esigne so that vehicles can reasonably an safely travel through the TTC zone with a spee limit reuction of no more than 10 mph. Although this may be a sensible recommenation, it is ifficult for the esigner to know what spee a river woul consier reasonable an safe given the work zone geometry. It is also mae clear in the MUTCD that reuce spee zoning [lowering the regulatory spee limit] shoul be avoie as much as practical because rivers will reuce their spees only if they clearly perceive a nee to o so (1). In other wors, a reuce poste spee limit may not be effective or appropriate if the visible roaway environment an poste spee are not complementary.. It is well known that vehicle operating spee is affecte by roa features an geometry. Preicting highway operating spees uner various scenarios is a useful precursor to appropriate regulatory an esign ecisions. However, reliable mathematical an statistical spee moels have proven elusive. This paper presents the evelopment of such a spee profile moel using ANN methoology. It has only been recently that Artifical Neural Networks (ANNs) have foun their way into the area of transportation ata analysis, an it seems that this moeling technique is well suite for such applications. First, the ata collection is presente. This is followe by the moel evelopment an results. DATA COLLECTION Spee an geometric ata were collecte from high-spee highway construction work zones. A high-spee highway was efine as roas an highways with free-flow operating spees of mph an higher (1). A construction work zone is efine as an area occupie for three or more ays for the purpose of constructing, reconstructing, rehabilitating or performing preventive maintenance (1). All sites were four-lane ivie freeways an typically interstate facilities; however, interstate look-alike facilities were also use. This stuy was limite to two typical work zone configurations: lane closures an meian crossovers. The following are efinitions of these two work zone types taken from (2). Meian crossover: a construction work zone strategy use on expressways (which inclue freeways) where: o the number of lanes in both irections are reuce, o at both ens, traffic in one irection is route across the meian to the oppositeirection roaway on a temporary roaway constructe for that purpose, Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 5 o bi-irectional traffic is maintaine on one roaway while the opposite irection roaway is close. Lane closure: a construction work zone technique for which one or more travel lanes an any ajacent shoulers are close to traffic. This technique is often employe as part of a reuction in number of lanes work zone strategy. Although meian crossovers an lane closures may have ifferent lane configurations, the ata collection an moeling apply only to facilities meeting these efinitions. Data were collecte from 10 ifferent construction work zone sites throughout the state of Pennsylvania an 7 sites throughout the state of Texas. All sites were carefully selecte so that they represente stanar an typical configurations. Work zones with an excessive number of interchanges were avoie because interchange presence may involve vehicle interaction moeling which was not the goal of this research. The spee profile of a traveling vehicle is continuous in nature; therefore, an ieal moel woul involve using a continuous representation of this profile. Such an approach woul require tracking the spee of many vehicles through the entire length of a work zone with each vehicle having its own unique profile for the particular site. Available methos of ata collection, however, make it ifficult to capture this profile as a continuous function. Therefore, measure spees were capture only at particular locations or points throughout a work zone site. Data were collecte from a total of 119 locations or points (excluing 17 upstream points) in 17 work zones, with an average of 7 ata points per site. Points were selecte in an effort to cover the range of all preictor variables. This was accomplishe through the following steps. First a vieo log was create for each work zone. Then the vieo was reviewe an the work zone was ivie into uniform sections with regars to the preictor variables. Depening on the length of the work zone, this resulte in anywhere from 4 to uniform sections. Finally, selection of these uniform sections was mae to best represent the range of geometric an roasie conitions present in the work zone. Upstream spee ata was collecte from all work zones. This was typically 2-3 miles upstream from the lane taper outsie of the influence of any traffic control evices in the avance warning area. It is important to note that the upstream spee was use as an input to the moel rather than an aitional point. Spee measurements were also taken at the center of the lane taper for all work zones. Both geometric an spee ata were collecte from the locations escribe above. Descriptions of all variables use in the moel can be seen in Table 1. Spee ata was collecte using LIDAR an raar guns. Approximately 200 vehicle spees were measure at each ata collection point. In orer to ensure that spee measurements represente a river s response to the input variables an not a response to vehicle interactions, only free-flow spee measurements were taken. This was efine, for the purpose of this research, as vehicles with time heaway greater than 4 secons from the vehicle ahea. For each vehicle spee measure, it was note whether the vehicle was a passenger car or truck. Trucks were efine as vehicles having more than two wheel axels. Summary statistics for all variables can be seen in the Tables 1 through 5 below. Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 6 TABLE 1 Input Variable Descriptions Variable Description WZ Configuration Lane closure; Meian crossover WZ Location Taper; Within Work Zone Length Distance from Beginning of Work Zone (Measure from the Lane Taper) Poste Spee Poste Spee Limit Roaway Type Permanent; Temporary R Raius of Horizontal Curve VA Flat; Upgrae; Downgrae; Crest Curve; Sag Curve TWW Travele Way With RSW Right Shouler With LSW Left Shouler With TPW Total Pave With RSDL Roasie Device on Left (None; Drum; Vertical Panel; Other Soft; Guarrail; Barrier; Opposing Traffic w/ No Separation) Loffset Offset from Travele Way of Roasie Device on Left RSDR Roasie Device on Right (None; Drum; Vertical Panel; Other Soft; Guarrail; Barrier; Opposing Traffic w/ No Separation) Roffset Offset from Travele Way of Roasie Device on Right Upstream Spee Spee Upstream from Avance Warning Area Previous Spee Previous Measure (or Preicte) Spee Previous Length Distance from Previous Measure (or Preicte) Spee Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 7 TABLE 2 Categorical Variables Work Zone Closure Crossover Configuration 42.9% 57.1% Work Zone Location Roaway Type Vertical Alignment Roasie Device Left Roasie Device Right Taper Within WZ 19.3% 80.7% Permanent Temporary 74.8% 25.2% Flat Upgrae Downgrae Crest Sag 37.8% 21.8% 26.1% 9.2% 5.0% None Drum Vertical Panel Other Soft Guarrail Barrier Opposing Traffic 38.7% 11.8% 1.7% 0.0% 3.4% 42.9% 1.7% Vertical Other Opposing None Drum Guarrail Barrier Panel Soft Traffic 36.1% 21.0% 8.4% 7.6% 7.6% 19.3% 0.0% TABLE 3 Continuous Variables Variable Mean Stanar Deviation Minimum Maximum Number of Samples Length (mi) 2.46 2.96 0 10.64 119 Poste Spee (mph) 59.96 7.09 119 Raius (ft) 99.34 3158.15 1911 11480 48 TWW (ft) 13.33 2.93 11 24 119 RSW (ft) 3.93 4.2 0 16 119 LSW (ft) 3.33 4.15 0 36 119 TPW (ft) 19.89 5.18 12 48 119 Loffset (ft) 3.6 8.96 0 48 73 Roffset (ft) 2.47 3.47 0 24 76 Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 8 TABLE 4 Data points in work zone (incluing taper) 85th Percentile Spee Summary Statistics (MPH) Variable Mean Stanar Deviation MinimumMaximum All Vehicles 62.06 5. 44 74 Cars 62. 5.71 43 76 Trucks.69 5.09 44 TABLE 5 Upstream Spees 85th Percentile Upstream Spee Statistics (MPH) Variable Mean Stanar Deviation MinimumMaximum All Vehicles 73 4.20 59 78 Cars 72.16 6.97 51 79 Trucks.88 3.41 75 MODEL DEVELOPMENT Artificial neural networks (ANNs) have successfully been employe by researchers over the past 25 years in solving a wie variety of engineering problems. However, it has only been recently that ANNs have foun their way into the area of transportation ata analysis. ANN structure an methoology is loosely base on the biological nervous system which consists of many interconnecte neurons (3). ANNs operate on a much smaller scale but use the same basic principles. As with the biological nervous system, ANNs consist of many interconnecte but artificial neurons which weight, sum an threshol incoming signals to prouce an output. Information is store within the strengths of the interconnections or weights. Figure 1 epicts a typical ANN architecture. Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 9 FIGURE 1 General Structure of a Fee-forwar ANN. Just as new memories are forme in biological neural systems through ajustments in the synaptic connection strengths, new memories are forme in ANNs by ajusting the weighte connections between neurons. This is typically one through well establishe training proceures wherein the network is presente pairs of input/output ata an an attempt is mae to search for a global minimum on the error surface over the space of the network parameters or weight values. Figure 2 emonstrates the basic training process. FIGURE 2 Network Training (4). Some avantages of using ANN that are particularly relevant to moeling complex relationships are: 1. No assumptions nee to be mae on the form of the moel 2. It is capable of extracting non-linear variable interactions Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 10 3. It is able to generalize from small training ataset In this research, the ANN moel was evelope using the input variables an measure 85 th percentile spees. ANN was use to fin an appropriate functional mapping between the inputs (geometric variables) an the output (85 th percentile operating spee). A block iagram of the moel evelope can be seen in Figure 3. u WZ (x) (0) ANN MODEL (x) DELAY FIGURE 3 Block Diagram of Spee Profile Moel. The output of the moel is the spee of a vehicle,, as a function of istance, x, measure from the beginning of the work zone or lane taper. The moel preicts spees only for locations of x for which an input vector is efine. The ANN moel preicts vehicle spee base on three inputs. The first input, u (x), is a vector containing the geometric variables at the WZ particular location. Some of these variables, like work zone type, are constant for a particular site, while most variables change epening on the particular point within the site. The secon input, (0), is upstream spee. This is the estimate spee of a vehicle prior to entering the work zone an is typically 2-3 miles upstream from the lane taper an outsie of the influence of the work zone traffic control. The upstream spee is use in preicting all other spees within the work zone. The final input is the previous preicte spee which is fe back from the moel output through a istance elay block. For the first spee preicte in a work zone, the previous preicte spee is the upstream spee, (0). It is important to note that istance to the previous preicte spee is inclue in u wz (x). It is necessary to inclue this variable since ata collection points were not equally space. Before eveloping an ANN moel, input variables were transforme through a variable encoing process. Categorical variables were encoe using a binary representation which is typical in neural network implementation. For example, a variable containing N categories was represente using N separate binary inputs. This is a common technique which avois the orering of inputs an keeps categories inepenent from one another. Variables with only two categories were represente with a single binary input. In aition to the variable encoing, both raius of curvature an the istance to the previous spee measurement were inverte in orer to represent these quantities Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 11 within a finite range. The variables Loffset an Roffset were set to an arbitrary large value in cases where there was no roasie evice on that sie of the roaway. Inputs were normalize in a manner that the mean was zero an the stanar eviation was one. Such normalization techniques are commonly employe to increase learning rates an reuce training time. RESULTS The Neural Network Toolbox in MATLAB was use to evelop the ANN moel. Network inputs an targets were first normalize using the PRESTD comman in MATLAB. The first step in training the network is separating the ataset into two groups; one for training the network, an the other for testing the network. Because of the limite number of ata points available, the testing ataset neee to be carefully selecte such that it was representative set. A total of 5 sample points out of the total of 119 was chosen for testing. The top two plots in Figures 4 to 6 isplay results for the training ataset in a slightly ifferent manner. The plot on the left has preicte spee on the vertical axis an measure spee on the horizontal axis. If the preictions were perfect, these ata points shoul be locate along the ashe line that has a slope equal to one. Regression was performe for the actual ata points an correlation coefficients were calculate. The plot on the right shows measure spee an preicte spee for each training ata point. The results were sorte in ascening orer (increasing values) of measure spee. A mean square error (MSE) for the training ata set is also isplaye in the plot. The testing ata results are isplaye in a similar manner below the training results. The results obtaine using the 85 th percentile atasets for cars, trucks an all vehicles are shown in Figures 4 to 6. Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 12 te ic P re te ic P re 80 R = 0.904 R = 0.98 Data Points Best Linear Fit Perfect Preiction Measure Spee Training Data Network Performance MSE= 6.0632 80 Data Points Best Linear Fit Perfect Preiction 40 40 80 Measure Spee Testing Data Network Performance MSE= 6.3372 ph ) (m ph ) (m Measure Spee Preicte Spee 40 0 20 40 80 100 120 Training Point Number Measure Spee Preicte Spee 1 2 3 4 5 Testing Point Number FIGURE 4 ANN Results for Car Moel R = 0.876 Training Data Network Performance MSE= 5.8936 Measure Spee Preicte Spee te ic P re te ic P re ph ) (m Data Points 45 Best Linear Fit 45 Perfect Preiction 40 40 40 0 20 40 80 100 120 Measure Spee Training Point Number Testing Data Network Performance MSE= 4.4174 Measure Spee R = 0.946 Preicte Spee Data Points Best Linear Fit Perfect Preiction 45 45 Measure Spee ph ) (m 45 1 2 3 4 5 Testing Point Number FIGURE 5 ANN Results for Truck Moel Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 13 Training Data Network Performance MSE= 6.8959 75 R = 0.879 75 Measure Spee Preicte Spee te ic P re te ic P re Data Points 45 Best Linear Fit 45 Perfect Preiction 40 40 80 Measure Spee Testing Data Network Performance MSE= 5.6952 R = 0.908 Data Points Best Linear Fit Perfect Preiction Measure Spee ph ) (m ph ) (m 40 0 20 40 80 100 120 Training Point Number Measure Spee Preicte Spee 1 2 3 4 5 Testing Point Number FIGURE 6 ANN Results for Moel with All Vehicles Figure 7 isplays the effect of poste spee an five geometric variables on preicte spee. The five geometric variables consiere are work zone configuration, crest curve, sag curve, length an total pave with (TPW). Preicte spee in miles per hour is shown on the vertical axis an the variable values are shown on the horizontal axis. While stuying the effect of one input variable, all other inputs were fixe at their average value. It is to be note that for categorical variables only values 0 an 1 have a physical meaning. Original paper submittal not revise by author.
Taylor, Muthiah, Kulakowski, Mahoney an Porter 14 FIGURE 7 Influences of Some Input Variables on Preicte Spee Original paper submittal not revise by author.
Taylor, Kulakowski, Muthiah, Mahoney an Porter 15 The traine ANN moel was then implemente in an easy to use EXCEL spreasheet. The user can input the esire values for the input variables, an a spee vs. istance plot is simultaneously generate. A screenshot of the program is shown in Figure 8. FIGURE 8 EXCEL Spee Profile Moel CONCLUSIONS Recent esign consistency stuies suggest that spee profiles can be use as a metho for etecting safety problems with roa features. It was the goal of this research to evelop a spee profile moel that will enable esigners to etect esign inconsistencies in high-spee highway construction work zone esigns before implementation. An artificial neural network moel was successfully evelope for preicting 85 th percentile spees of cars an trucks separately. The moels were evelope using geometric ata an spee ata collecte from ten ifferent work zones throughout the state of Pennsylvania an seven work zones in the state of Texas. The final moel was then implemente into an EXCEL spreasheet. Suggestions for future work inclue eveloping a larger ataset to improve moel performance. Although the moel performe well on this particular ataset, it is recommene that further testing be one to valiate the moel on a wie variety of work zones. It is possible that ifferent mappings exist between geometric variables an 85 th percentile spee epening on the particular samples use for training. In aition to more testing, future ata collection methos shoul be more representative of a continuous spee profile. If more ata points were Original paper submittal not revise by author.
Taylor, Kulakowski, Muthiah, Mahoney an Porter 16 collecte at closer intervals throughout the work zones, it is likely that a more accurate moel coul be evelope. ACKNOWLEDGEMENTS This research was fune by the National Cooperative Highway Research Program. Original paper submittal not revise by author.
Taylor, Kulakowski, Muthiah, Mahoney an Porter 17 REFERENCES 1. Mahoney, K.M., Porter, R.J., Kulakowski, B.T., Elefteriaou, L., Lee, D.U., Ullman, G.L., Miaou, S-P, an Pezolt, V. Design of Construction Work Zones on High-Spee Highways. NCHRP 3-69 First Interim Report, Transportation Research Boar, National Research Council, Washington, DC (2004). 2. Mahoney, K.M., Porter, R.J., Taylor, D.R., Kulakowski, B.T., an Ullman, G.L. Design of Construction Work Zones on High-Spee Highways. NCHRP 3-69 Secon Interim Report, Transportation Research Boar, National Research Council, Washington, DC (2005). 3. Hagan, M.T., Demuth, H.B., & Beale, M., Neural Network Design, PWS Publishing Company, 1996 4. Demuth, H.B., an Beale, M. Neural Network Toolbox User s Guie : For use with MATLAB, The Mathsworks, Inc., Natick MA., 2004. Original paper submittal not revise by author.