clustering-neural network models for freeway work zone ... - CiteSeerX

International Journal of Neural Systems, Vol. 14, No. 3 (2004) 147–163 c World Scientific Publishing Company

CLUSTERING-NEURAL NETWORK MODELS FOR FREEWAY WORK ZONE CAPACITY ESTIMATION XIAOMO JIANG and HOJJAT ADELI Departments of Biomedical Informatics, Civil and Environmental Engineering and Geodetic Science and Neuroscience, The Ohio State University, 470 Hitchcock Hall, 2070 Neil Avenue, Columbus, Ohio 43210 USA [email protected]

Two neural network models, called clustering-RBFNN and clustering-BPNN models, are created for estimating the work zone capacity in a freeway work zone as a function of seventeen different factors through judicious integration of the subtractive clustering approach with the radial basis function (RBF) and the backpropagation (BP) neural network models. The clustering-RBFNN model has the attractive characteristics of training stability, accuracy, and quick convergence. The results of validation indicate that the work zone capacity can be estimated by clustering-neural network models in general with an error of less than 10%, even with limited data available to train the models. The clustering-RBFNN model is used to study several main factors affecting work zone capacity. The results of such parametric studies can assist work zone engineers and highway agencies to create effective traffic management plans (TMP) for work zones quantitatively and objectively. Keywords: Backpropagation; freeway workzone; intelligent transportation system; radial basis function neural network; traffic Engineering.

1. Introduction

integrates judiciously the mathematical rigor of traffic flow theory with the adaptability of neural network analysis. In a recent article, Adeli and Jiang4 present a new neuro-fuzzy model for estimating the work zone capacity taking into account seventeen different numeric and linguistic factors. A backpropagation neural network is employed to estimate the parameters associated with the bell-shaped Gaussian membership functions used in the fuzzy inference mechanism (Zadeh,16 ). An optimum generalization strategy is used in order to avoid over-generalization and achieve accurate results. Comparisons with two empirical equations demonstrate that the new neurofuzzy model has the following advantages:

The work zone capacity in freeways is usually defined as the mean queue discharge flow rate at a freeway work zone bottleneck (any constricted location that restricts the flow of vehicles in a work zone) (HCM, 2000). The work zone capacity is a complicated and non-quantifiable function of a large number of interacting variables some of which are linguistic such as work zone layout and weather conditions, which explains the dearth of scientific work on mathematical modeling of the freeway work zone capacity. Karim and Adeli13 present an adaptive computational model for estimating the work zone capacity and queue length and delay taking into account the following factors: number of lanes, number of open lanes, work zone layout, length, lane width, percentage trucks, grade, speed, work intensity, darkness factor, and proximity of ramps. The model

(1) it incorporates a large number of factors impacting the work zone capacity,

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(2) it provides a more accurate estimate of the work zone capacity, especially when the data for factors impacting the work zone capacity are only partially available, and (3) unlike the empirical equations, the new model does not require subjective selection of various adjustment factors or values by work zone engineers based on prior experience. However, the existing models for freeway work zone capacity estimation cannot yield the required accuracy with limited data available to train the models. In this research, the subtractive clustering approach is judiciously integrated with the radial basis function (RBF) and backpropagation (BP) neural network models to create the clustering-RBF and clustering-BF neural network models. The two clustering-neural network models are developed for estimating the work zone capacity in a freeway work zone as a function of seventeen different factors. The clustering-RBFNN model investigated in this research is a modification of the fuzzy-RBFNN model of Karim and Adeli.13 Work zone patterns are first grouped into similar clusters using a data clustering approach. Similarity of any new work zone pattern to the training patterns is measured by its proximity to the centers of the clusters. Karim and Adeli13 use the fuzzy c-means algorithm (Adeli and Karim,5 ) to find the cluster centers. In this work, the subtractive clustering approach described in Adeli and Jiang4 is used to determine the optimum number of clusters and clustering centers where it is assumed that each data point belongs to a potential cluster based on the minimum value of a predefined objective function. Subtractive clustering is an effective approach for grouping data into clusters and discovering structures in data (Chiu,9 Yager and Filev,15 ). The clustering-BPNN model is similar to the clustering-RBFNN model except that the neural network classifier in the former is the simple BP algorithm and in the latter is the RBFNN.

(1) percentage of truck (x1 ), (2) pavement grade (vertical slope in the longitudinal plane) (x2 ), (3) number of lanes (x3 ), (4) number of lane closures (x4 ), (5) lane width (x5 ), (6) work zone layout (x6 ), (7) work intensity (x7 ), (8) work zone length (length of closure) (x8 ), (9) work zone speed (x9 ), (10) proximity of ramps (x10 ), (11) work zone location (x11 ), (12) work zone duration (x12 ), (13) work time (x13 ), (14) work day (x14 ), (15) weather condition (x15 ), (16) pavement conditions (x16 ), and (17) driver composition (x17 ). A detailed discussion of impact of these factors is presented in Adeli and Jiang.4 Symbolically, the work zone capacity can be expressed as a function of 17 variables defined in the previous paragraphs: y = f (x1 , x2 . . . , x17 )

(1)

Among the seventeen variables, some are linguistic such as work zone layout and weather conditions, some are binary two-valued parameters such as the interchange effect representing the existence of ramps near or within work zone, and others are numeric such as the work zone length. The variables are quantified and normalized using the methods described in Adeli and Jiang.4 Spline-based nonlinear functions are used to quantify each linguistic as well as binaryvalued variable mathematically. Spline-based nonlinear functions are also assigned to numeric variables in order to model the impact of their variations on the work zone capacity. 3. Clustering-Neural Network Models

2. Factors Impacting the Work Zone Capacity Seventeen different numeric and linguistic factors are used in the developed clustering-neural network models:

3.1. General topology of neural networks Artificial neural networks have been shown as a powerful tool for solution of complicated problems not amenable to conventional mathematical approaches (Adeli and Hung;3 Adeli;1 Adeli and Karim6 ; Adeli

Clustering-Neural Network Models for Freeway Work Zone Capacity Estimation

q0=1(bias) q1 q2

1

x1 Z-shape

1

0

1

0

S-shape 1

Input Quantification and Normalization (18 variables)

x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18

Input layer Fig. 1.

p0=1 (bias) w0,j

q3 q4

p1

q5 q6 q7

p2

q8 q9 q10 q11 q12 q13 q14 q15 q16 q17 q18

w0 w1

149

Cˆ = Estimated work zone capacity N = Number of clusters pj = jth variable in the hidden layer qi = ith normalized input variable wi,j = Weight of the link connecting the ith normalized input node to the jth node in the hidden layer wj = Weight of the link connecting the jth node in the hidden layer to the output node xi = ith input variable

w2 N

wi,j

wj

Cˆ = ∑ p j w j j =0

wN-1 pN −1 wN pN

S-shaped spline-based nonlinear function Z-shaped spline-based nonlinear function Bias node Input node Normalized input node Hidden node

w18,N

Hidden layer

Topology of the neural network models for estimating the work zone capacity.

Figure 1 Topology of the neural network models for estimating the work zone capacity 7

and Park ). The topology of the neural network models for estimating the work zone capacity is presented in Fig. 1. It consists of an input layer, a hidden layer, and an output layer. The input layer has 18 nodes representing the 17 variables defined in the previous section and an 18th node to indicate the data collection locality. The values of the variables in the input layer are normalized to values between 0 and 1 employing the S-shape and Z-shape spline-based nonlinear functions as explained in Adeli and Jiang.4 The normalization prevents the undue domination of variables with large numerical values over the variables with small numerical values, thus improving the accuracy of estimating work zone capacity and accelerating the convergence of the network training. The normalized variables are denoted by q1 to q18 in Fig. 1. A bias node with the value of one (q0 = 1) is added to the input layer. Without the bias, the hyperplane separating the patterns is constrained to pass through the origin of the hyperspace defined by the inputs, which limits the adaptability of the neural network model. The parameter wij represents the

weight of the link connecting the normalized input node i to node j in the hidden layer The number of nodes in the hidden layer, N +1, is 26 equal to the number of cluster centers used to characterize and classify any given training data set. For the number of nodes in the hidden layer, instead of the trial-and-error approach commonly used in creating the neural network topology, the subtractive clustering method described in Adeli and Jiang4 is used. In Fig. 1, the variables in the hidden layer are denoted by p1 to pN . A bias node with the value of one (p0 = 1) is also added to the hidden layer for the same reason described earlier. The output layer has only one node for the estimated work zone capacˆ is obtained ity. The estimated work zone capacity, C, from the clustering-neural network model as the aggregation of the weighted outputs of N + 1 hidden nodes as follows: Cˆ =

N X

wj p j

(2)

j=0

where the first term in the summation (for j = 0) represents the bias and wj is the weight of the link

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Hidden layer (RBF layer)

Input layer

Output layer

p 0 = 1 (bias)

q1

 q − c1 p1 = exp  2σ 12 

q2

 q − c2 p 2 = exp  2σ 22 

   

2

w0 w1

2

N

   

Cˆ = ∑ p j w j j =0

w2

M

M

wN  q −cN p N = exp  2σ N2 

q18

2

   

Legend Bias pj

Normalized input node

jth node of the RBF (hidden) layer (j = 1, 2, …, N) Data transmission/clustering

Link connecting the RBF nodes to the output node

cj = Vector of the jth clustering center Cˆ = Estimated work zone capacity σ j = Influencing range of the Gaussian function N = Number of clusters pj = jth radial basis function (j = 1, 2, …, N) qi = Normalized variables affecting work zone capacity (i = 1, 2, …,18) q = Vector of normalized input variables w = Weight of the link connecting the jth node in the hidden layer to the output node Fig. 2. Architecture of the clustering-RBFNN model for estimating the work zone capacity. Figure 2 Architecture of the clustering-RBFNN model for estimating the work zone capacity

connecting the jth node in the hidden layer to the output node.

3.2. Clustering-RBFNN Adeli and Karim5 used the fuzzy c-means clustering algorithm to improve the performance of RBFNN for another pattern recognition problem, the freeway traffic incident detection problem. Karim and Adeli13 present a fuzzy-RBFNN model for mapping eleven quantifiable and non-quantifiable factors in-

fluencing the work zone capacity27to the work zone capacity. In this work, the Gaussian function is used as basis in the hidden or the radial basis function (RBF) layer of the neural network model in the following form (Fig. 2): ! kq − cj k2 pj = exp j = 1, 2, . . . , N (3) 2σj2 pP 2 where kXk = 18 |Xi | is the Euclidean distance, pj is the value of the jth node in the hidden layer, q is the 18 × 1 vector of the normalized input vari-


ables, cj (j = 1, . . . , N ) is the 18×1 vector of the jth clustering data center, which are determined by the subtractive clustering approach, as are the optimum number of clusters, and N is the number of radial basis functions which is also equal to the optimum number of clusters. In Eq. (3), the factor σj is the influencing range of the Gaussian function centered at cj , whose squared value in this research is approximated using the mean squared distance between cluster centers, as expressed by: σj2 =

M 1 X kcj − ci k2 N i=1

j = 1, 2, . . . , N

(4)

where M is the total number of training data sets. The work zone capacity estimated by the clusteringRBFNN model is obtained as the aggregation of the weighted outputs of N + 1 hidden nodes from Eq. (2). The weights of the links connecting the hidden nodes to the output node are updated by minimizing the mean squared error (MSE) of the normalized work zone capacity and using the gradient descent optimization algorithm described in Adeli and Jiang.4 Two stopping criteria are used for convergence of the clustering-RBFNN model. One is the acceptable mean squared error value (0.001 used in this study) and the other is the maximum number of iterations (400 used in this study). In a conventional RBFNN, the weights of the links connecting the input layer to the hidden layer (i.e., the RBF parameters cj defining the cluster centers) have to be updated in every iteration, similar to a standard multiple-layer feed-forward neural network. In contrast, in the clustering-RBFNN model used in this research, the centers of RBF clusters (cj ) are determined in one step using the subtractive clustering approach, resulting in substantial speedup in the training convergence of the network and reduction of computer processing time for training the network. 3.3. Clustering-BPNN The BP neural network (Hagan et al.,11 ) has been popular because of its simplicity despite its slow convergence rate for complex pattern recognition problems (Adeli and Hung,2 ). It is based on the gradient descent unconstrained optimization approach where

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weights are modified in a direction corresponding to the negative gradient of a backward-propagated error measure. In this research, the simple BP neural network algorithm is integrated with the subtractive clustering technique and used as an alternative approach for estimation of work zone capacity. The output of the jth hidden node in the BP neural network, pj , is determined by the sigmoid activation function (Fig. 3): pj = 1/(1 + exp(−Xj )) j = 1, 2, . . . , N (5) P18 where Xj = i=0 wij qi is the aggregation of the 18 weighted normalized input variables plus the bias (for i = 0). The output value estimated by the clustering-BPNN model is obtained also using the sigmoid activation function as follows: Cˆ = 1/(1 + exp(−X)) (6) PN where X = j=− wj pj is the aggregation of the weighted outputs of N nodes in the hidden layer plus the bias (for j = 0). Figure 3 shows the architecture of the clusteringBPNN model for the work zone capacity estimation. There are a number of differences between this model and the clustering-RBFNN model shown in Fig. 2. In the clustering-BPNN model: (1) weights of the links connecting the input layer to the hidden layer are required to be updated in each iteration of training the network, (2) aggregation is executed in both hidden and output layers, (3) a so-called momentum term is added to the weight modification equation or learning rule to help prevent the neural network getting trapped in a local minimum (Hagan et al.,11 ), and (4) the over-generalization problem is avoided by employing an optimum generalization strategy (Adeli and Jiang4 ) for training the neural network. The resulting clustering-BPNN model requires more computation time for estimating the work zone capacity compared with the clustering-RBFNN model. 4. Training and Validating the Networks 4.1. Training The data used to train and validate the neural network models are collected primarily from the literature and complemented by data obtained directly

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Hidden layer (BP layer)

Input layer

Output layer

p 0 =1 (bias) q0 =1 (bias) w0,1 w0,N

w0,2 w1,1

q1

18

X 1 = ∑ wi ,1q i i =0

w1,N

p1 w0

Neuron 1

w1,2 w1

w2,1 w2,2

q2

18

X 2 = ∑ wi , 2 qi

p2

i =0

w2

j =0

Neuron 2

w2,N

N

∑w

j

pj

Cˆ

Σ wN

M

M w18,1

w18,2

q18 w18,N

18

X N = ∑ wi , N qi

pN

i =0

Neuron N

Legend Bias

Normalized input node

pj

Sigmoid activation function output for the jth node in the hidden layer

Cˆ

Estimated work zone capacity

Hidden node Link connecting nodes Sigmoid activation function

Cˆ= Work zone capacity value in the output layer N = Number of clusters pj = jth sigmoid function (j = 1, 2, …, N) qi = Normalized variables affecting work zone capacity (i = 1, 2, …,18) wi,j = Weights of the link connecting the ith input node to the jth hidden node wj = Weights of the link connecting the jth hidden node to the output node Fig. 3. 3Architecture the work work zone zone capacity capacity. Figure Architectureofofthe theclustering-BPNN clustering-BPNN model model for for estimating the

from North Carolina Department of Transportation. The collected data sets from four different states and city of Toronto are divided randomly into training, checking, and validation data set, as summarized in Table 1. Limited data from California (from the late 1960’s) and Ohio were also available to the authors but are not included in this study because those from California are too old and those from Ohio are

too few to represent typical work zones. 28 None of the data set includes all the 17 input variables used in the new computational model. The number of input variables provided ranged from four (number of lanes, number of lane closure, work zone intensity, and work zone duration) to fourteen (percentage of heavy trucks, grade of pavement, number of lanes, number of lane closure, work zone intensity, length


Table 1.

153

0.1 Training, checking, and validation data set. 0.09

State

Mean squared error

520.08 Data Sets

Index

Training

Indiana Maryland North Carolina Texas Toronto

1 2 3 4 5

9 9 7 7 7

Total

39

5

0.07 Checking 0.06 0.05 0.04 1 0.03 1 0.02 1 0.01 0

1 1

1

Checking data sets Training data sets

Validation

Point of optimum generalization

2Iteration number 1960 (minimum 2point of checking data curve) 1 2 1

1400 1960 2100 0

700

8

2800

3500 4200 4500 Iteration number

0.1 0.09 0.08

Checking data sets

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

Training data sets Point of optimum generalization Iteration number 1960 (minimum point of checking data curve)

1

700

1400 1960 2100 0

2800

3500 4200 4500 Iteration number

a) Clustering-BPNN (a) Clustering-BPNN

Fig. 4.

0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

Training data sets

1

30

60

90

120 150 Iteration number

b) Clustering-RBFNN (b) Clustering-RBFNN

Convergence curves for training the clustering-neural network models.

0.1 0.09 0.08 closure,

of work zone speed, proximity of ramps to 0.07 work zone, work zone location, work zone duration, Training data sets 0.06 work 0.05time, work day, weather conditions, and driver 0.04 composition). For those unavailable input variables, 0.03 of zero are obtained after variable quantificavalues 0.02 tion and normalization, as described earlier. 0.01 Training of neural networks is performed similar 0 1 90 30 120 150 60 to the approach used in Adeli and Jiang4Iteration and skipped number for the sake of brevity. b) Convergence results for trainClustering-RBFNN ing the networks based on the entire 39 training data sets in Table 1 are displayed in Fig. 4. It is noted that the convergence rate for the clustering-RBFNN Figure 4 Convergence curves for training the clustering-neural network models is substantially faster than the clustering-BPNN. On a 1.5 GHz Intel Pentium 4 processor, the CPU time for training the former is 0.25 seconds and the latter 1.42 seconds. Mean squared error

Mean squared error

Mean squared error

a) Clustering-BPNN

4.2. Validation Eight sets of validation data sets selected randomly from the collected data sets are used to validate the accuracy of the clustering-neural network models

Figure 4 Convergence curves for training the clustering-neural network models

(Table 1). The input values for the 8 data sets are summarized in Table 2. There are two sets from the states of Indiana, Maryland and Texas each, and one set from North Carolina and Toronto each. The work zone capacities estimated by three different models, the neuro-fuzzy logic (Adeli and Jiang4 ), clustering-BPNN, and clustering-RBFNN models, are summarized in Table 3. The root of mean squared error (RMSE) values obtained for the three models are 229 vph, 215 vph, and 114 vph, respectively. As such, based on the limited training and validation data used, the clustering-RBFNN model provides the most accurate results. The error percentage for this model ranges from 0.1% to 8.7% (with one exception the error is generally under 5%). For the 29 other two approaches, the error is in general less than 10% with the exception of one case for each method. The clustering-RBFNN model appears to have the attractive characteristics of training stability (the training results are not sensitive to the initial selections of the weights), accuracy, and quick

29

154 X. Jiang & H. Adeli

Table 2. Var.

x1

x2

x3

Input values for 8 work zone scenarios used to validate three work zone capacity estimation models.

x4

x5

x6

x7

x8

x9

x10

x11

x12

x13

x14

x15

x16

x17

Speed (km/h)

Ramp

Location

Work dur.

Work time

Work day

Weather Cond.

Pave. Cond.

Driver Comp.

State

– – 48 34 – – – –

– – Yes Yes – – – –

Rural Rural Urban Urban Rural – – Urban

Long Long Short Short Long Short Short Short

Day Day Day Night Day – – Day

Weekday Weekday Weekday Weekday Weekday – – –

– – Sunny Sunny – – – Sunny

– – – – – – – Dry

– – 0 0 – – – 1

Indiana Indiana Maryland Maryland N. Carolina Texas Texas Toronto

Data Set

Truck (%)

Grade (%)

No. of Lanes

No. of Lane Closures

Lane Width

Layout

Work Intensity

Length of Closure (km)

1 2 3 4 5 6 7 8

32 10 8 8.5 26.2 – – –

– – 5 0 – – – 3

2 2 4 4 2 4 5 3

1 1 1 2 1 1 3 1

– – – – – – – –

M C – – – – – –

6 2 1 6 6 1 3 –

11.7 11.7 0.18 2.2 – – – –

M = Merging, C = Crossover, – Unavailable data

x18

Table 3.

Comparisons of the work zone capacity estimates by neuro-fuzzy logic, clustering-BPNN, and clustering-RBFNN models.

Measured

Neuro-Fuzzy Logic î ) (vph) (C (Adeli & Jiang, 2003)

Clustering-BPNN (Cî ) (vph)

Clustering-RBFNN (Cî ) (vph)

Open Lanes

Closed Lanes

Value (Ci ) (vph)

Values (vph)

Error (%)

Values (vph)

Error (%)

Values (vph)

Error (%)

Indiana

1 2

1 1

1 1

1308 1595

1320 2138

0.9 34.1

1326 1265

1.4 20.7

1287 1540

1.6 3.4

Maryland

3 4

3 2

1 2

5205 2456

5343 2652

2.6 8.0

4982 2624

4.3 6.8

5211 2588

0.1 5.4

North Carolina

5

1

1

1284

1290

0.5

1287

0.2

1264

1.6

Texas

6

3

1

4590

4649

1.3

4200

8.5

4563

0.6

7

2

3

2680

2900

8.2

2779

3.7

2914

8.7

8

2

1

3904

3779

3.2

4039

3.5

3793

2.8

Toronto

Root mean square error =

v u 8 uX u (Cî − Ci )2 u t i=1 8

229

215

114


Data Set Number

State

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convergence. In the next section, the clusteringRBFNN model is used to perform a parametric study of the main factors affecting the work zone capacity.

studies presented in this paper, however, are for eleven factors influencing the work zone work intensity: percentage of trucks, work zone configuration, layout, weather conditions, pavement conditions, work zone lane width, pavement grade, presence of ramps, work day, and work time. The impact of other factors is not investigated because insufficient data existed in the neural network training data set available to the authors.

5. Parametric Studies of Work Zone Capacity This study is done for an actual freeway work zone scenario with measured data provided in Dixon et al.10 The work zone site is a two-lane rural freeway on I-95 in North Carolina with one lane closure [Fig. 5(a)]. Dixon et al.10 provide values for only nine out of seventeen input variables used in the computational models created in this research, as summarized in Table 4. Data are not provided for pavement grade, lane width, work zone length, work zone speed limit, proximity to a ramp, weather and pavement conditions, and driver composition. Parametric

5.1. Work intensity Work intensity in the parlor of the freeway work zone is a qualitative and subjective concept without any standard classification scheme. In this research, the work intensity is divided into six categories from the lightest to the heaviest, represented numerically by one to six, respectively, as summa-

(a) Work zone configuration

1

Work intensity 3 4

2

5

6 1600

1600 Variation curve with percentage of trucks

Work zone capacity (vphpl)

1550

1550

1500

1500

1450

1450

1400

1400

1350

1350

1300

Variation curve with work intensity

1300


156

1250

1250

1200

1200 01

4

8

12

16

20

24

28

Percentage of trucks (%) (b) Variation curves Fig.5 5. Variation of work capacity intensity percentage of trucks. Figure Variation of work zonezone capacity withwith workwork intensity and and percentage of trucks (The top horizontal axis represents work intensity and the bottom horizontal axis represents percentage of trucks)


Table 4.

157

Work zone capacity variations with work intensity and percentage of trucks.

State: North Carolina Location: Rural Number of lanes: 2 Number of lane closures: 1 Work intensity: 6 Work time: day Measured work zone capacity: 1284 vphpl Work intensity Capacity (vphpl)

1 1522

Percentage of trucks (%) Capacity (vphpl)

8 1548

2 1515 12 1513

Work duration: Long-term Truck percentage: 26.2 Workday: weekday

3 1505 16 1409

4 1342 20 1314

24 1268

5 1276

6 1265

26.2 1265

30 1264

Work intensity: 1 = Lightest, 2 = Light, 3 = Moderate, 4 = Heavy, 5 = Veryheavy, 6 = Heaviest Table 5.

Classification of work zone intensity.

Intensity Level

Qualitative Description

Work Type Examples

1 2 3 4 5 6

Lightest Light Moderate Heavy Very heavy Heaviest

Median barrier installation or repair Pavement repair Resurfacing Stripping Pavement marking Bridge repair

rized in Table 5. Keeping all other variables in the given work zone constant, the work zone capacities for six different work intensities are estimated using clustering-RBFNN model. The results are summarized in Table 4 and displayed in Fig. 5(b), which shows the work zone capacity reduces with an increase in the intensity of the work, as expected. 5.2. Percentage of trucks Keeping all other variables in the given work zone constant, the work zone capacities for nine different percentages of truck, ranging from 8% to 30%, are estimated. The results are summarized in Table 4 and displayed in Fig. 5(b), which shows the work zone capacity reduces with an increase in the percentage of trucks, as expected. The measured value provided by Dixon et al.10 for the truck percentage of 26.2 is 1284 vphpl. The clustering-RBFNN model provides the estimate of 1265, with a small error of less than 2%. 6. Work Zone Configuration, Layout, and Weather/Pavement Conditions Parametric studies of work zone configurations include the total number of lanes (2, 3 or 4), number

of lane closures (1, 2 or 3), and work zone layout (i.e., merging, shifting, and crossover). Further, the influence of weather conditions (i.e., rainy or snowy) and pavement conditions (i.e., wet or icy) on the work zone capacity are also investigated. The work zone configurations are shown in Fig. 6 and their results are summarized in Table 6 and graphically shown in Fig. 7. Three different work zone scenarios are studied. Scenario 1 is for a two-lane freeway with one-lane closure, Scenario 2 is for a three-lane freeway with two-lane closure, and Scenario 3 is for a four-lane freeway with three-lane closure (Fig. 6). In all scenarios only one lane is open. The results are summarized in the Table 6. For a single open lane, the work zone capacity reduces as the total number of lanes increases. Compared with a two-lane freeway, this reduction is only 1% for a three-lane freeway, but 9% for a four-lane freeway. This suggests that for a four-lane freeway a cost-benefit analysis should be performed for the option of keeping two lanes open versus maintaining just one lane open. The results of parametric studies indicate that the work zone capacity varies significantly with the number of freeway lanes as well as number of lane closures which is

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One closure

Shifting Merging (a) Merging with one lane closure in two lane freeway

(b) Shifting in two lane freeway

Crossover

(c) Crossover

Three closures

Two closures

(d) Two closures in three-lane freeway Fig. 6.

(e) Three closures in four-lane freeway Work zone configuration and layout.

Figure 6 Work zone configuration and layout consistent with the study on freeway work zones in Texas by Krammes and Lopez.14 The per lane work zone capacity for the merging layout is about 14% more than that for the crossover layout and about 8% more than that for the shifting layout. The work zone capacity for the sunny weather (dry pavement) condition is about 6% more than that for the rainy weather (wet pavement) and about 10% more than that for the snowy weather condition.

6.1. Work zone lane width and pavement grade Keeping all other variables in the given work zone constant, the work zone capacities for seven different lane widths, ranging from 2.7 m (9 ft) to 3.6 m (12 ft) in increments of 0.15 m (0.5 ft) are estimated for two cases, in the presence and absence of the pavement grade. The results are shown in Table 7 and graphically in Fig. 8. In the presence of the pavement grade, the estimated work zone capacity 31


Table 6.

Variation of work zone capacities with influencing factors.

Factors

Scenarios

No. of Lanes

No. of Lane Closures

Estimated Capacity (vphpl)

Work zone configuration

1 (8a) 2 (8d) 3 (8e)

2 3 4

1 2 3

1287 1274 1171

Scenarios

Layout


1 (8a) 2 (8b) 3 (8c)

Merging Shifting Crossover

1287 1193 1112

Scenarios

Weather Condition

Pavement Condition


1 2 3

Sunny Rainy Snowy

Dry Wet Snowy/Icy

1287 1213 1159

Work zone layout

Weather/ Pavement


1

2

3

1300

1300

1280

1280

1260

1260

1240

1240

1220

1220

1200

1200

1180

1180

Work zone configuration Work zone layout Weather/pavement conditions

1160 1140

159

1160 1140

1120

1120

1100

1100 1

2

3

Scenario No. Figure Variation work zone capacities with configuration, work zone configuration, zone layout, and Fig. 7. Variation of 7work zone of capacities with work zone work zone work layout, and weather/pavement weather/pavement conditions conditions.

ranges from 1054 vphpl (for the smallest lane width of 2.7 m) to 1342 vphpl (for the largest lane width of 3.6 m). In the absence of the pavement grade, the estimated work zone capacity ranges from 1262 vphpl (for the smallest lane width of 2.7 m) to 1862 vphpl

(for the largest lane width of 3.6 m). The following observations are made. The work zone lane widths in the range of 3.3 m (11 ft) to 3.6 m (12 ft) (the U.S. standard lane width) do not affect the work zone capacity by any significant measure. As the work

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Table 7.

Work zone capacities with lane width and pavement grade.

Lane Width (m) (m)

Estimated Work Zone Capacity (vphpl) With Pavement Grade Without Pavement Grade

2.70 2.85 3.00 3.15 3.30 3.45 3.60

1054 1132 1225 1294 1327 1339 1342

1262 1422 1615 1761 1830 1856 1862

Lane width 2.7m ~ 3.6m

(a) Configuration


2.70

2.85

3.00

3.15

3.30

3.45

3.60

1900

1900

1800

1800

1700

1700

1600

1600 Absence of pavement grade

1500

1500

1400

1400

1300

1300

1200

1200 Presence of pavement grade

1100 1000 2.70

1100 2.85

3.00

3.15

3.30

3.45

1000 3.60

Work zone lane width (m)

(b) Variation curves Figure 8 Variation ofofwork lane width andand pavement grade Fig. 8. Variation workzone zonecapacities capacitieswith with lane width pavement grade.

zone lane width reduces the work zone capacity decreases significantly. The presence of the work zone pavement grade exacerbates the traffic flow constriction (e.g., speed) and affect drivers’ behaviors, re-

sulting in a significant reduction in the work zone capacity in the range of 20% for a work zone lane width of 2.7 m (9 ft) to 39% for a width of 3.6 m (12 ft).

33


6.2. Presence of ramp The neural network models take into account the effect of presence of ramps on the work zone capacity. The presence of ramps is treated as a qualitative

variable instead of a quantitative one. An example of ramp proximity to the work zone is illustrated in Fig. 9(a). The work zone capacities estimated for a two-lane rural freeway on I-95 in North Carolina with one lane closure in the presence and absence

Ramp

(a) Configuration 1400

1400 Absence of ramp

1300

1300

Work zone capacity

Weekday during daytime 1200

1200 Weekday at night Presence of ramp

1100

1100 Work day/work time Ramp

1000

1000

Weekend during daytime 900

900 Weekend at night

800

800 1

2

Scenarios No. 3

4

(b) Variation curves Fig. 9.Figure Variation of workofzone capacities with workday and work time as time well as zone location 9 Variation work zone capacities with workday and work as work well as work zone and ramp.

location and ramp Table 8.

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Work zone capacities with influencing factors.

Group

Scenarios

Location

Ramp


Work zone Location/ramp

3 4

Rural Rural

No Yes

1287 1143

Group

Scenarios

Work Time

Workday


Work day/time

1 2 3 4

Daytime Night Daytime Night

Weekday Weekday Weekend Weekend

1287 1164 934 847

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X. Jiang & H. Adeli

of a ramp are summarized in Table 8 and shown in Fig. 9(b). The presence of ramp reduces the capacity by 12.6%. 6.3. Work day and work time Work zone capacities for four combinations of work day (weekday or weekend) and work time (daytime or night) are summarized in Table 8 and presented in Fig. 9(b). Since in all likelihood commuters and regular travelers during the weekdays are more familiar with the configuration of the work zone and the traffic control plans in the affected areas (e.g., route diversion) than non-commuters (e.g., tourists) traveling during the weekends, the work zone capacity is somewhat larger during the weekday than during the weekend. The parametric study performed in this research can quantify this observation. The estimated capacities for the weekend are about 37% smaller that those for the weekday during both daytime and night. The driver behavior and traffic characteristics differ during daytime and nigh time. Night construction can decrease the work zone capacity because of the reduced travelers’ attention and inferior visibility during nighttime (Al-Kaisy and Hall8 ). Again, the results performed in this research can quantify this observation. The estimated work zone capacities for construction at night are 10–11% smaller that those for the construction at daytime. 7. Final Comments The results of validation indicate that the work zone capacity can be estimated by clustering-neural network model in general with an error of less than 10%, even with limited data available to train the models. With additional data and training of the models the accuracy can be improved substantially. The computational models presented in the paper are general. The parametric studies, however, are based on the adaptation of the work zone in a two-lane rural freeway on I-95 in North Carolina with one lane closure. There is no intention to offer generalized conclusions for every other work zone situation. However, the computational models provide a powerful tool to perform parametric studies for other work zone situations. The results of a parametric study of the factors impacting the work zone capacity can assist work zone engineers and highway agencies to create effective TMPs for work zones quantitatively and ob-

jectively. To the authors’ best knowledge this quantitative parametric study is the first of its kind. A number of observations are made based on the limited data available for training the models. There is a definite need to collect additional data for various work zone conditions. Such data will have two significant applications. First, they can be used to further train the clustering-neural network models in order to improve the accuracy of work zone capacity estimation. Second, they can be used for more detailed sensitivity analysis. Acknowledgment This manuscript is based on a research project sponsored by the Ohio Department of Transportation and Federal Highway Administration. The assistance of Mr. Randy Perry of North Carolina Department of Transportation in providing traffic data for training and testing the neural networks is greatly appreciated. References 1. H. Adeli, Neural networks in civil engineering – 1999–2000, Computer-Aided Civil and Infrastructure Engineering 16(2) (2001) 126–142. 2. H. Adeli and S. L. Hung, An adaptive conjugate gradient learning algorithm for effective training of multilayer neural networks, Applied Mathematics and Computation 62(1) (1994) 81–102. 3. H. Adeli and S. L. Hung, Machine Learning — Neural Networks, Genetic Algorithms, and Fuzzy Sets (John Wiley and Sons, New York, 1995). 4. H. Adeli and X. M. Jiang, Neuro-fuzzy logic model for freeway work zone capacity estimation, J. Transportation Engineering 129(5) (2003) 484–493. 5. H. Adeli and A. Karim, A fuzzy-wavelet RBFNN model for freeway incident detection, J. Transportation Engineering, ASCE 126(6) (2000) 464–471. 6. H. Adeli and A. Karim, Construction Scheduling, Cost Optimization, and Management — A New Model Based on Neurocomputing and Object Technologies (Spon Press, London, 2001). 7. H. Adeli and H. S. Park, Neurocomputing for Design Automation (CRC Press, Boca Raton, Florida, 1998). 8. A. Al-Kaisy and F. Hall, Effect of darkness on the capacity of long-term freeway reconstruction zones, in Proc. 4th Int. Symp. Highway Capacity, Transportation Research Circular E-C018 (Maui, Hawaii, 2001), pp. 164–174. 9. S. Chiu, Fuzzy model identification based on cluster estimation, J. Intelligent & Fuzzy Systems 2(3) (1994) 267–278.


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estimation, J. Transportation Engineering, ASCE 129(5) (2003) 494–503. 14. R. A. Krammes and G. O. Lopez, Updated capacity values for short-term freeway work zone lane closure, Transportation Research Record No. 1442, Transportation Research Board, National Research Council (Washington, D.C., 1994), pp. 49–56. 15. R. R. Yager and D. P. Filev, Approximate clustering via the mountain method, IEEE Transactions on Systems, Man and Cybernetics 24(8) (1994) 1279–1284. 16. L. A. Zadeh, Fuzzy set as a basis for a theory of possibility, Fuzzy Sets and Systems 1(1) (1978) 3–28.