Application of Adaptive Neuro-Fuzzy Inference System for Road

KSCE Journal of Civil Engineering (2013) 17(7):1761-1772 Copyright ⓒ2013 Korean Society of Civil Engineers DOI 10.1007/s12205-013-0036-3

Transportation Engineering

pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205

Application of Adaptive Neuro-Fuzzy Inference System for Road Accident Prediction Mehdi Hosseinpour*, Ahmad Shukri Yahaya**, Seyed Mohammadreza Ghadiri***, and Joewono Prasetijo**** Received January 17, 2012/Revised October 23, 2012/Accepted January 8, 2013

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Abstract Since the last two decades, several modeling approaches have been developed in road safety literature to establish the relationship between traffic accidents and road characteristics. However, to the best of the authors’ knowledge, no extensive research work has been published on application of Adaptive Neuro-fuzzy Inference System (ANFIS) on road accident modelling. Therefore, the present paper aims to develop an ANFIS technique for modelling traffic accidents as a function of road and roadside characteristics. To achieve the objective, accident data and road characteristics were collected over a two-year period along the Qazvin-Loshan intercity roadway in Iran. The candidate set of explanatory variables included the Mean Horizontal Curvature (MHC), Shoulder Width (SW), Road Width (RW), Land Use (LU), Access Points (AP), Longitudinal Grade (LG), and Horizontal Curve Density (HCD). The results showed that RW, SW, LU, and AP significantly affected accident frequencies. Using statistical performance indices, the ANFIS model was compared with the Poisson, negative binomial, and non-linear exponential regression models. Based on the comparative results, the proposed model had higher prediction performance than the other three traditional models which has been widely used in the literature. To conclude, the proposed model could be used as a robust approach to handle uncertainty and complexity existed in accident data. In general, ANFIS model can be an effective tool for transportation agencies since intervention decisions and plans aiming at improving road safety depend on the prediction capabilities of a system. Keywords: ANFIS, accident prediction models, comparative measures, best subsets ··································································································································································································································

1. Introduction Since the last few decades of the 20th century, the world has experienced large increases in motorization and urbanization that have propelled increases in the number of traffic vehicles and transportation infrastructures. Since more and more communities have been provided with these facilities, a rapid increase in road accidents has been recorded as a result of the growth in road traffic intensity. According to the World Health Organization (WHO), more than 1.17 million people die in road accidents around the world every year, about four deaths every three seconds. Every year, over 10 million people are disabled or injured from road accidents. More than 6 million will die and as much as 60 million will be injured during the next 10 years in developing countries unless urgent action is taken. Moreover, a joint study undertaken by the WHO, Harvard University, and the World Bank showed that traffic accidents were estimated to be the world's ninth most important health problem in 1990. The

study estimated that, by the year 2020, road accidents would move up to third place in the table of leading causes of death and disability that affect the world community (WHO, 1999). This warning statistic clearly shows that road accidents present serious problems in society. Road safety authorities invest considerable efforts into reducing accident costs by providing road safety improvements (e.g., geometry improvement, traffic control, and enforcement). They are interested in identifying accident-prone locations as well as those factors (e.g., road geometry, traffic, etc.) that affect accident occurrences in order to develop road safety countermeasures as effective as possible. Realistically speaking, the success of such improvements depends on reliable and dependable approaches that properly identify the most relevant factors that affect accident likelihood and frequency. The main goal of these methods is to quantify the safety effects of road geometry elements and traffic information on accident occurrences. In general, most studies have shown that road accidents are complex and rare events; from another

*Ph.D. Student, School of Civil Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Pulau Penang, Malaysia (Corresponding Author, E-mail: [email protected]) **Associate Professor, School of Civil Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Pulau Penang, Malaysia (E-mail: [email protected]) ***Lecturer, Dept. of Transportation Engineering, Malaysia University of Science and Technology, 47301 Petaling Jaya, Kuala Lumpur, Malaysia (E-mail: [email protected]) ****Senior Lecturer, School of Civil Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Pulau Penang, Malaysia (E-mail: [email protected]) − 1761 −

Mehdi Hosseinpour, Ahmad Shukri Yahaya, Seyed Mohammadreza Ghadiri, and Joewono Prasetijo

point of view, the relationship between accident frequency and road traits are often complicated. These findings have led safety researchers to use predictive models in which the dependent variable is the accident frequency or accident rate (Brijs et al., 2007; Montella et al., 2008). There are several approaches to develop accident prediction models. Statistical methods are commonly used in most previous works (Miaou and Lum, 1993; Maher and Summersgill, 1996; De Leur and Sayed, 2002; Zhang and Ivan, 2005; Ramirez et al., 2009). For example, Ivan and O'Mara (1997) developed Poisson regression model for the prediction of traffic accidents using the Connecticut Department of Transportation’s accident data. Results of the model suggested that posted speed limit and annual average daily traffic are critical predictive variables, leading to the conclusion that Poisson regression model is preferred to linear regression model. Martin (2002) described the relationship between crash rate and traffic Volume per Hour (VH) and the influence of traffic on crash severity. A negative binomial distribution was used. Lord et al. (2008) used the ConwayMaxwell-Poisson (COM-Poisson) Generalized Linear Model (GLM) for modeling motor vehicle crashes. Their results showed that the COM-Poisson GLM offers a better alternative over the negative binomial regression for modeling motor vehicle crashes. Recently, in addition to statistical approaches, soft computing techniques like Artificial Neural Networks (ANNs), Fuzzy Logic (FL), and Hybrid Fuzzy Neural Network (FNN) have been used to provide effective and robust modelling in transportation engineering (Kumara et al., 2003). These techniques are also called nonparametric approaches since they don’t have any predefined assumption for modelling events. They can be used in place of statistical modelling techniques in which the later cannot be used either due to insufficient number of data or some restrictive assumptions. For conventional parametric models, any deviation from their distributional assumptions may result in biased parameter estimations; in such cases, it is difficult to establish a plausible model (Tortum et al., 2009). On the other hand, nonparametric models learn from the real data without the use of an analytical relationship between input and output variables. This is a promising advantage of nonparametric models because the relationship between traffic accidents and explanatory variables is more often a complex interaction and also is uncertain in nature (Awad and Janson, 1998). In road safety literature, some researchers who used ANNs to establish models for relating accident occurrence to a set of roadway traits, including road geometrics, roadside features, and traffic flow (Abdelwahab and Abdel-Aty, 2001; Chiou, 2006) while some others utilized fuzzy logic in their studies (Sayed et al., 1995; Schretter, 1996). Awad and Janson (1998), for instance, explained the superiority of nonparametric regression techniques for predicting accident occurrence. The authors used both neural network and fuzzy logic methodologies to predict truck accidents on freeway ramps. Mussone et al. (1999) developed ANNs to establish a model for relating Accident Index (AI) to roadway conditions, visibility, weather, and the characteristics of vehicles and drivers in Milan. Adeli and Karim (2000) developed a multi-

paradigm intelligent system approach for freeway incident detection using integrated fuzzy, wavelet, and neural computing techniques. They also used fuzzy c-means clustering to extract significant information from the observed data and reduce its dimensionality. The authors indicated that the new model produced excellent incident detection rates with no false alarms when tested using both real and simulated data. Akgüngör and o Dog an (2009) proposed an ANN model and a Genetic Algorithm (GA) approach to estimate the number of accidents (A), fatalities (F), and injuries (I) in Ankara, Turkey. The results of model comparison showed that the ANN model outperformed the GA model. To investigate the performance of the ANN model for future estimations, a fifteen-year period from 2006 to 2020 with two possible scenarios was employed. Kumara et al. (2003) evaluated safety improvements at signalized intersection approaches by nonparametric regression in Singapore. They first used fuzzy subtractive clustering to derive a homogeneous dataset from the original noisy data. This clustered dataset was eventually used to predict hazardousness. The results implied that the nonparametric regression approach works properly in multidimensional measurement spaces, in which hazardousness is assumed to be a function of several geometric, traffic, and traffic control measures. Viswanathan et al. (2006) developed a model for automatic incident detection by applying neuro-fuzzy techniques; the results indicated that the proposed model enhances accuracy of incident detection in a given arterial road. To the best of the authors’ knowledge, very little research has been reported in the literature on the application of an adaptive neuro-fuzzy approach for road safety modelling, while statistical tools have been commonly used in such cases. From the literature review, it is observed that ANFIS has been widely used in transportation engineering (e.g., Pribyl and Goulias, 2003; Andrade et al., 2006; Tortum et al., 2009; Sangole et al., 2011; Mucsi et al., 2011; Al-Ghandoor et al., 2012). However, the application of ANFIS in traffic accident modelling is still limited. In response, this study aims at employing this non-parametric technique for evaluating the safety effects of road geometric and environmental characteristics on accident frequencies. Another aim of this study is to investigate predictive capability of the ANFIS model by comparing its performance results with those obtained from Poisson, negative binomial, and nonlinear exponential regression models using accident data on 65-km segments during two years period between 2006 and 2007. The organization of this paper is as follows: Section 2 explains the ANFIS model and structure. Section 3 discusses the framework of the proposed model for road accident prediction. The results are presented in Section 4, and the conclusions and recommendations are presented in Section 5.

2. Adaptive Neuro-fuzzy Inference System (ANFIS) ANFIS, which was developed by Jang (1993), is a universal approximator that incorporates Sugeno-type fuzzy inference systems into adaptive neural networks. By applying the adaptive capability of ANNs in tuning rule-based fuzzy systems, ANFIS

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KSCE Journal of Civil Engineering

Application of Adaptive Neuro-Fuzzy Inference System for Road Accident Prediction

2.1 Layer 1 Each node in this layer is an adaptive node with node functions described as: O1, i – µ A( x )

i = 1, 2

for

O1, i – µ B ( y )

i = 3, 4

for

i–2

(3) (4)

where x and y are the input to nodes, A and B are the linguistic labels, µ A ( x ) and µ B ( y ) are the membership functions for Ai and Bi-2 fuzzy sets, respectively. There are various membership functions (such as trapezoidal, triangular, Gaussian function) which can be applied to determine the membership grades. In this study, the Gaussian function given below was used: i

i–2

⎧ x – c 2⎫ O1, i = µ ( x ) = exp⎨ –⎛ -----------i⎞ ⎬ ⎝ σi ⎠ ⎩ ⎭ Fig. 1. (a) A Two-input First-order Sugeno Fuzzy Model with Two Rules, (b) Equivalent ANFIS Architecture (Jang,1996)

uses the power of the two patterns: ANNs and fuzzy logic in a single framework and overcomes their own shortcomings simultaneously. Such framework makes the ANFIS modelling more systematic and less dependent on expert knowledge. Studies based on this approach have shown that neuro-fuzzy systems are more effective for dealing with uncertain human behaviors because of their flexible and adaptive capability. Moreover, they also have the ability to handle large amounts of noisy data from dynamic and non-linear systems (Çaydaçs et al., 2009). Using a learning process, ANFIS can give the mapping relation between an input and output dataset to determine the optimal distribution of membership functions, which involve a premise and a consequent part (Ying and Pan, 2008). The ANFIS architecture is shown in Fig. 1; each layer involves several nodes that are described by a node function. The inputs of the present layers are obtained from the nodes in the previous layers. To illustrate the procedures of an ANFIS, it is assumed two inputs (x, y) and one output (f) are used in this system. For a first-order Sugeno fuzzy model, a common rule set with two fuzzy if–then rules is as follows (Jang, 1996): Rule 1 : If x is A1 and y is B1 , then f1 = p1x + q1y + r1

(1)

Rule 2 : If x is A2 and y is B2 , then f2 = p2x + q2y + r2

(2)

where x and y are the inputs of model, A and B are the fuzzy sets, fi is a first order polynomial and represents the output of the rule ith, and pi, qi and ri are the consequent parameters to be settled. Figure 1(a) illustrates the fuzzy reasoning mechanism based on first-order Sugeno fuzzy model. The corresponding equivalent ANFIS architecture is shown in Fig. 1(b). Node functions in the same layer are of the same function family as described below. Note that Oj,i denotes the output of the ith node in layer j. Vol. 17, No. 7 / November 2013

(5)

where { ci , σi } is the parameter set that changes the shapes of the membership function. Parameters in this layer are referred to as the “premise parameters”. 2.2 Layer 2 Every node in this layer is a fixed node, marked by a circle node and labelled Π. It multiplies the incoming signals and outputs the product. O2, i = ω = µ A ( x ).µ B ( y ) i

i

for

i = 1, 2

(6)

The output signal ω i denotes the firing strength. The number of nodes for this layer equals the number of fuzzy ‘‘if-then’’ rules in the fuzzy inference system. 2.3 Layer 3 Every node in this layer is a fixed node, marked by a circle and labelled N. The ith node calculates the ratio of the ith rule’s firing strength to the sum of all rules’ firing strength. ωi ωi = ---------------O3, i = ω i = ---------ω ω + ω2 i 1 ∑

for

i = 1, 2

(7)

2.4 Layer 4 Every node in this layer is an adaptive node, marked by a square, with node function: O4, i = ω i .fi = ω i. ( pi x + qi y + ri ) for i = 1, 2

(8)

where fi is the output of the rule ith. 2.5 Layer 5 The single node in this layer is a fixed node. It computes the overall output as the summation of all incoming signals by: O5, i = fout =

∑ iω i.fi = overall output

(9)

Figure 1(b) shows that, given the values of the premise parameters, the overall output f can be expressed as a linear combination of the consequent parameters. Based on this observation, ANFIS

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uses a hybrid-learning algorithm, which is a combination of the backpropagation and least-squares methods, to update the parameters and learn the fuzzy model. In other words, ANFIS uses backpropagation algorithm for learning the parameters of membership functions and conventional least-squares estimator for estimating the parameter of first-order polynomial of the Takagi-Sugeno fuzzy model. There are two passes in the hybrid learning procedure for ANFIS. In the forward pass of the hybrid-learning algorithm, consequent parameters are identified by least-squares estimates. In the backward pass, the error rates propagate backward, the premise parameters are updated by the gradient descent, and the premise parameters are updated by the gradient descent algorithm. When the values of the premise parameters are fixed, the overall output can then be expressed as a linear combination of the consequent parameters: ω2 ω1 - f1 + ---------------- f2 = fout = ω 1 f1 + ω 2 f2 = ---------------ω1 + ω2 ω1 + ω2 ( ω 1x )p1 + ( ω 1 y )q1 + ( ω 1 )r 1 + ( ω 2 x )p2 + ( ω 2 y )q2 + ( ω 2 )r2 (10) where p1, q1, r1, p2, q2, r2 are consequent parameters. Generally, ANFIS maps input characteristics to input membership functions, input membership function to rules, rules to a set of output characteristics, output characteristics to output membership functions, and the output membership function to a single-valued output or a decision associated with the output (The MathWorks, 2001).

3. Application of ANFIS Model for Road Accident Prediction 3.1 Study Area and Data Collection To test the applicability and appropriateness of ANFIS technique for modeling accident frequency, one needs to choose a roadway as the study area for this research work. After inspecting several roadways, an intercity roadway located between Qazvin and Loshan in northern Iran was finally selected. This roadway, which is 75 km long, connects Qazvin and Guilan Provinces

Fig. 2 Map of Qazvin-Loshan Intercity Roadway

(Fig. 2). The roadway experiences high accident frequencies mainly due to poor road design and adverse weather conditions. It contains a wide variety of road geometric and environmental characteristics, and passes through industrial and residential areas, though most parts of the road are rural. The terrain through the roadway varies from nearly flat at the beginning of the roadway to rolling in the middle and mountainous at the end of the road. Besides, some parts of the roadway were separated by median barriers or small physical obstacles, while most parts are not physically separated. The number of lanes in each direction varies from one to two. Some sections of the road, especially those in mountainous terrain, have climbing lanes to allow lowspeed vehicles to travel without slowing traffic following them. The study area consisted of a 65 km stretch of the roadway and divided into 1-km fixed length segments. Data on road geometric and environmental characteristics were collected from field observations. A number of roadway characteristics such as road width, number of driveways and minor intersections, and land use were obtained by visual inspections. Meanwhile, data on road geometric such as shoulder width, horizontal curvature, and vertical slope were obtained from actual measurements along the roadway. Information on traffic volumes through the roadway were collected from the Iranian Road Maintenance and Transport Organization (IRMTO). The data consisted of all vehicular traffic and were counted by loop detectors located in the middle of the road. The extracted traffic data act as a representative measure of exposure for the whole roadway due to two reasons: (i) traffic counters were not available for other parts of the road; (ii) most of travelling vehicles negotiated the roadway from the beginning to the end of the route. As such, traffic data were not considered in this study because all the road segments under study come from the same road with nearly fixed traffic flow. Accident data were collected from the police reports for the years of 2006 to 2007. More than one year of accident data was used in order to prevent possible fluctuations in accident frequencies. In the police reporting system, accidents were located in terms of distance from where they occurred to the nearest kilometre post, thus the 1-km scale served as the sampling unit for all considered segments. During the two-year period, a total of 880 accidents occurred in the considered segments. They ranged from 3 to 57 with an average of 13.5 accidents per two-year period. Finally, the data on road geometric and environmental characteristics were merged to accident data based on the kmpost of accidents and the beginning and ending of each road segment. The road characteristics used for model estimation includes Mean Horizontal Curvature (MHC), Shoulder Width (SW), Road Width (RW), Land Use (LU), Access Points (AP), Longitudinal Grade (LG), and Horizontal Curve Density (HCD). 3.2 Model Input and Output Variables In order to decide which subsets of independent variables should be included in the modelling process, “best subset algorithm” was used. According to this algorithm, the best subsets are identified based on some specified criteria without

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Table 1. Summary Description of Road Characteristics Variable Road Widths Shoulder Widths Land Use Access Points Horizontal Curvature Longitudinal Grade Horizontal Curve Density

Symbol RW SW LU AP MHC MLG HCD

Description Widths of the two sides of the roadway (m) Sum of the left and right shoulders of the roadway (m) Location of the roadway (the level of roadside development) The number of driveways per km Weighted mean of horizontal curvature (km−1) Weighted mean of longitudinal grade (%) The number of horizontal curves per km

Mean 12.56 2.28 0.1 1.29 1.37 5.18 1.6

Variance 17.38 0.72 0.05 2.93 0.88 12.37 2.15

Table 2. Results of Variable Selection Process No. of Variables 1 1 2 2 3 3 4 4 5 5 6 6 7

C-p 35.1 36.8 17.4 17.7 8.2 9.2 3.3 7.3 4.2 4.8 6 6.1 8

Selection Criteria AIC 443.71 444.89 430.84 431.12 422.55 423.53 417.3 421.56 418.01 418.7 419.8 419.96 421.79

BIC 450.24 451.41 439.54 439.82 433.42 434.4 430.34 434.61 433.23 433.92 437.19 437.35 441.36

LU X

X X X X X X X X X X

requiring the fitting of all of the possible subset regression models. In fact, these algorithms search for all possible subsets to ultimately select the subset that meets the criterion (criteria). This method is applicable when the pool of potential X variables is not large; otherwise, stepwise regression procedures may be used to assist in variable selection (Kutner et al., 2004). In this study, the decision on whether to select the best subsets is based on three criteria, namely the Akaike Information Criterion (AIC), Mallows’ Cp, and Bayesian Information Criterion (BIC). The subset with the lowest values based on these criteria will be selected as the best subset. The results of the selection process are shown in Table 2. According to the mentioned criteria, the best subset includes the variables Land Use (LU), Road Width (RW), Access Points (AP), and Shoulder Width (SW). The variables Longitudinal Grade (LG), Horizontal Curve Density (HCD), and Horizontal Curvature (MHC) were found to be insignificant, and then excluded from predicting the crash frequency. 3.3 Training and Checking Data Sets After discarding non-significant variables, the available data was divided randomly into training (80%: 52 records) and checking datasets (20%: 13 records). The training set was assigned to build the ANFIS model, while the checking dataset was used to ensure that the trained model is a suitable representation of the target system and also to avoid overfitting of the system to the training dataset. Overfitting occurs when the model is trained too much Vol. 17, No. 7 / November 2013

RW

X X X X X X X

SW

X X X X X X X X X X X

Input Variables AP

HCD

MHC

LG

X X

X X X X X X X X

X X X X X

X X

X X X

such that the mapping between the input and output data has lost its generalization capability to fit any data that it was not trained on (Bishop, 1995). A Chi-squared test was used to check whether or not the accident frequency distributions between training and checking subsets are different. The test showed that the difference between the subsets are not statistically significant (p-value = 0.46). 3.4 ANFIS Model Construction The construction of ANFIS involves two steps. The first step is fuzzification, which aims to establish an initial fuzzy inference system and to select a structure for the ANFIS model by determining the number of membership functions per input variable, type/shape of the membership functions for both the premise and parts of each rule. The subtractive clustering method was used to partition the universe of discourse for input variables and to generate the fuzzy inference system. This technique is an improved form of the mountain clustering method and proposed by Chiu (1994). The method assumes each data point can be as a potential cluster center and estimates a measure of the likelihood that each data point would be the cluster center, based on the density of surrounding data points. The steps of this algorithm can be summarized as: (1) select the data point with the highest potential to be the first cluster center, (2) remove all data points in the vicinity of the first cluster center as determined by the range of influence (radius), and (3) iterate on this process until all

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of the data is within the radii of a cluster center (Tortum et al., 2009). The purpose of clustering is to determine the minimum number of fuzzy rules required for FIS construction and their associated membership parameters. The clustering partitions input data set into a number of groups named cluster so that the similarity is high for inter-group and low for intra-group members. The cluster centres are used here as the basis of the ANFIS IF-THEN fuzzy rules, where the premise membership functions are the Gaussian function and the consequent MFs are the first order Takagi-Sugeno type of FIS. The next step includes training the parameters of the constructed fuzzy inference system for minimizing the Root Mean Square Error (RMSE) and adjusting the shape of the membership functions. The hybrid learning algorithm was used to develop the ANFIS model. This algorithm consisted of backpropagation for the parameters associated with the input membership functions and leastsquares estimation for the parameters associated with output membership functions. During the learning process, ANFIS uses simultaneously training and checking datasets to avoid overfitting. Training of the ANFIS may be stopped by two measures. Based on the first measure, by assigning an error tolerance, the learning process will be stopped when the training data error remains within this tolerance. In the second measure, learning stops when a maximum number for training iterations (epochs) is achieved. The act of continuing the training process may sometimes result in overfitting problem, which makes either the training or checking error function unsteady and produces increasing or fluctuating error functions. In the present study, ANFIS training is stopped if the error tolerance is close enough to 0, or if the number of training iterations reaches 100, whichever comes first. Moreover, the best ANFIS model is selected based on achieving a minimum RMSE for both the training and checking datasets,

where the RMSE is under control and not increasing (El-Shafie et al., 2007; Mousavi et al., 2007). All the process on this study was implemented at Fuzzy logic toolbox in MATLAB. To summarize, the overall flowchart of ANFIS model is shown in Fig. 3.

4. Results and Discussion 4.1 ANFIS Construction Based on the modelling process described earlier, the initial fuzzy inference system was constructed by subtractive clustering. The structure of the constructed initial fuzzy model was illustrated in Fig. 4. As seen in the figure, the fuzzy model contains three membership functions for each input, three Sugeno-type rules, and one output. The membership functions of the premise part are in the form of a Gaussian function, and the rule base consists of three rules. The consequent part is a linear function between the output variable and all the input variables. After the construction of the initial fuzzy inference system, the parameters associated with membership functions were tuned during the training process using hybrid learning algorithm. The main goal was to keep minimum the Root Mean Square (RMSE) values for training and checking datasets with the tuned set of parameters. For this purpose, several ANFIS models with four input parameters (LU, RW, SW and AP) and one output parameter (ACF) were constructed; the performance of each model was then considered. The best ANFIS model was ultimately found where the RMSE for the training dataset converged to a minimum of 4.3828, which led to the completion of the learning process. The network was then

Fig. 4. Constructed Fuzzy Model with 4 Inputs, 3 Rules, and 1 Output

Fig. 3 Flowchart of Model Construction

Fig. 5. ANFIS Model Structure − 1766 −



Table 4. Estimated Input Membership Parameters

Table 3. Rules has been Constructed Rule No. 1 2 3

Rules If (LU is Low) and (RW is Medium) and (SW is Narrow) and (AP is Low) then (ACF is Low) If (LU is Medium) and (RW is Narrow) and (SW is Wide) and (AP is Medium) then (ACF is Medium) If (LU is High) and (RW is Wide) and (SW is Medium) and (AP is High) then (ACF is High)

checked for overfitting during the training phase using the checking dataset. It was revealed that overfitting did not occur while the ANFIS model was being trained, and that the RMSE of the checking data reached a constant value of 4.38828. The constructed ANFIS model was shown in Fig. 5, and the 3 rules created were summarized in Table 3. According to the figure, the model architecture has a total of 12 nodes (3 × 4) for Layer 1, three nodes for Layer 2 (equal to the number of rules in the ANFIS), and three nodes for Layer 3, representing the consequent parameters of the linear function. The number of antecedent parameters, which represents the shape and spread of each fuzzy set for the input parameters, is 24 (4 × 3 × 2), as the Gaussian membership function is characterized by two parameters (c and σ). In Layer 3, the number of consequent parameters is 15 (3 × 5) because there are three linear membership functions in the output parameter and five consequent parameters (pi, qi, ki, li, ri) of the linear membership function. The input membership functions of the ANFIS model were shown in Fig. 6, and the parameters of these functions were listed in Table 4. The linguistic labels Low, Medium, and High were assigned for “LU” and “AP”, while Narrow, Medium, and Wide were assigned for “RW” and “SW”. The estimated parameters of the output functions were demonstrated in Table 5. When the membership functions representing LU and RW inputs are examined, the two membership functions of “Low” and “Medium” for LU and “Narrow” and “Medium” for RW nearly fit into one another. In this case, it could be thought that the two membership functions should be assigned for both variables. However, the prediction accuracy of the ANFIS model having two membership functions for each input was lower than that of the proposed

Estimated parameters [σ c] [0.178 0] [0.1838 0.0228] [0.1725 0.1977] [2.653 11] [2.648 12] [2.652 22] [0.5373 2] [0.5306 3] [0.5863 4] [1.765 0] [1.766 1] [1.767 2]

Membership

Low Medium High Narrow Road width (RW) Guassmf Medium Wide Narrow Shoulder width (SW) Guassmf Medium Wide Low Access points (AP) Guassmf Medium High *Guassmf, Guassian type of membership function Guassmf*

Land use (LU)

Table 5. The Estimated Consequent Parameters of Sugeno Linear Function: yi = pi × LU + qi × RW + ki × SW + li × AP + ri Membership function no (i) Output Low Medium High

The parameters of Sugeno linear function pi 15.38 -108.7 17.03

qi -2.280 -1.0020 0.8742

ki -5.067 4.488 -3.255

li 0.9545 -0.3530 0.1831

ri 47.03 5.081 -1.360

ANFIS model with three membership functions. 4.2 Model Comparison and Selection In order to validate the results of ANFIS model, it was compared to those of three statistical models including Poisson (PO), Negative Binomial (NB), and Non-linear Exponential (NLE) models. First, for a Poisson model, the probability of yi accidents occurring on segment i, Pr ( Y = yi ) , can be estimated by Eq. (11): (y i )

λi exp( –λi ) P( Y = yi ) = ---------------------------yi !

(11)

λi = exp( βXi )

(12)

where yi is number of accidents on section i (2006-2007); λi is

Fig. 6. Input Membership Functions Vol. 17, No. 7 / November 2013

Type of membership function

Input

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the mean accident frequency for section i, Xi is a vector of covariates, and β is a vector of estimable regression coefficients. The Poisson regression model is based on a restrictive assumption that the variance of accidents is equal to the mean (E[Yi] = Var[Yi]). However, in many cases, the variance is greater than the mean which is well known as over-dispersion. In such a case, applying a Poisson regression model would result in underestimation of the standard error of the regression parameters and a biased selection of covariates (Miranda-Moreno and Fu, 2006). Overdispersion is caused by unobserved heterogeneity across road segments due to variation in road geometric and environmental characteristics through the roadway. To deal with extra-variation in the accident data, a Negative Binomial (NB) model was proposed by including a gamma distributed error term in the Poisson model such that: λi = exp( βXi + εi )

(13)

Access Point (AP), Shoulder Width (SW), and Land Use (LU) were found to significantly contribute to accident frequencies while Road Width (RW) was only significant in the PO model. The dispersion parameter of the NB model (α) was highly significant (p-value < 0.001), implying the presence of overdispresion in the accident data. This may be due to extra variation in road geometric designs and environmental characteristics as well as unobserved effects related to seasonal variations and driver behaviors. The random effects associated with these unmeasured factors were explained by the gamma-distributed error term and the over-dispersion parameter in the NB model (Mitra and Washington, 2007). To test predictive performance of the ANFIS model compared to the above-mentioned models, three statistical measures were used. These measures include the Root Mean Square Error (RMSE), the Mean Relative Error (MRE), and the Variance Account For (VAF):

where the exp(εi) is gamma distributed with mean 1 and variance α (overdispersion parameter). The NB model takes the unobserved heterogeneity of the Poisson mean into account by allowing the variance to differ from the mean as below: 2

Var [yi ] = E [yi ][1 + αE[ yi ]] = E [yi ] + αE [yi ]

(14)

The distribution function for NB model is specified by Eq. (15): Γ ( yi + 1 ⁄ α ) ⎛ λi ⎞ y ⎛ 1 ⁄ α ⎞ 1 ⁄ α ------------------- ------------------Pr ( Y = yi ) = -------------------------Γ ( 1 ⁄ α )yi ! ⎝ λi + 1 ⁄ α⎠ ⎝ λi + 1 ⁄ α⎠ i

(15)

where Γ ( ⋅ ) is a value of gamma distribution. The maximum likelihood method was used to estimate the parameters of Poisson and NB models. The non-linear exponential regression model (NLE) is in the form of yi = ai exp ( bi xip ) where yi is the estimated accident frequency with normal error term, xip represents the input variables, and ai and bi are coefficients calculated by the regression. The regression parameters are estimated using the LevenbergMarquardt algorithm. For more details of the statistical models presented above, the reader is referred to Kutner et al. (2004) and Hilbe (2011). Table 6 presents the parameter estimates and their corresponding p-values for Poisson, NB, NLE models. From the table, it is observed that the sign and magnitude of coefficients for the three models are the same. The variables

2 1 N RMSE = ---- Σi = 1 ( yi – yˆ i ) N

(16)

1 N i – yi MRE( % ) = ---- ∑ i = 1 y----------N yi

(17)

var( yi – yi )⎞ VAF ( % ) = ⎛ 1 – -----------------------⎝ var ( yi ) ⎠

(18)

where yi is the observed value, yˆ i is the predicted value, “var” is the symbol for the variance, and N is the number of samples. The interpretation of these criteria is: the lower the RMSE and MRE, the better the model performs, and the higher the VAF, the better the model does. The results were summarized in Table 7. As seen in the table, the ANFIS yielded the best performance results among other three models in which its corresponding values of RMSE, MRE, and VAF are 4.38, 0.34, and 78.4%, respectively. This implies a considerable improvement in those

Table 7. Comparison of the Performance of ANFIS, PO, NB, and NLE Models Model ANFIS PO NB NLE

RMSE 4.383 5.294 5.510 5.237

MRE 0.3421 0.4395 0.4403 0.4383

VAF(%) 78.4 68.5 65.9 69.2

Table 6. Parameter Estimates of the Poisson (PO), Negative Binomial (NB), and Non-linear Exponential (NLE) Models Variable Intercept Land use (LU) Access points (AP) Shoulder width (SW) Road width (RW) Dispersion parameter (á)

Poisson Estimate 3.1843 0.7223 0.0633 -0.2699 -0.0167 -

NB p-value 0.000 0.000 0.008 0.000 0.051 − 1768 −

Estimate 3.1280 0.6788 0.0827 -0.2524 -0.0172 0.0917

NLE p-value 0.000 0.033 0.046 0.000 0.191 0.000

Estimate 27.283 0.7749 0.0431 -0.3085 -0.0178 -

p-value 0.000 0.000 0.087 0.000 0.129 -



Fig. 7. Comparison of Observed and Predicted Accident Frequencies by ANFIS, Poisson (PO), Negative Binomial (NB), and Nonlinear Exponential (NLE) Models

measures for the ANFIS model compared to the PO, NB, and NLE models which resulted in nearly identical results. It implies that the proposed model was able to suitably predict road accident frequencies. Fig. 7 demonstrates a comparison between observed and predicted ACFs by the ANFIS, PO, NB, and NLE models. The figure indicates that the ANFIS yields a significantly better fit for accident frequency than the other three models having very similar performance. This may be due to the complex nature of road accidents as well as inadequacy of the data used. 4.3 Interpretation of Estimated Parameters In this section, the interpretation of each predictor was presented. To do this, the results of parameter estimates for the ANFIS model as well as those from three statistical PO, NB, and NLE models were discussed. As an overall conclusion from Tables 5 and 6, the variables “AP” and “LU” have a positive effect on accident frequency while “SW” has a negative sign. Based on the ANFIS result regarding “RW” in Tables 3 and 5, this variable has a conflicting effect on accident frequency. More details regarding the effect of each variable were explained in the following. 4.3.1 Land Use Land use was found to be positively associated with the accident frequencies. This is consistent with expectation, which implies that road segments in developed areas are more likely to experience accidents than those located in semi or undeveloped areas. In fact, this variable act as a proxy to other unmeasured factors which potentially affect accident frequency, such as roadside activates related to parking and pedestrian movements, traffic flow, congestion, etc. 4.3.2 Access Points AP was found to be positively associated with accident frequencies, as expected. It has a negative impact on the safety of road segments; this is due to high conflicts between oncoming vehicles and vehicles entering from minor driveways into the through traffic. This finding is consistent with those in prior studies Vol. 17, No. 7 / November 2013

(Greibe, 2003; Zhang and Ivan, 2005; Kim and Washington, 2006). Preventive improvements with regards to access control and management techniques could be suggested to reduce the accidents relevant with access points. 4.3.3 Shoulder Width Shoulder width was found to decrease accident frequencies, which agrees with expectation because wider shoulders provide more recovery room for errant vehicles to take corrective action, and also to avoid encountering hazardous roadside objects as causes of accident occurrence (Milton and Mannering, 1998). 4.3.4 Road Width As seen in Tables 3 and 5, the relation between accident frequency and RW seems to be somewhat conflicting. The results of ANFIS model shows that the effect of road width on accident frequencies varies across the roadway. On the one hand, narrower road width is negatively associated with accident frequency (as given by negative sign of RW in Rules 1 and 2). This may be explained by the fact that higher accident frequencies in those segments are related to inadequate paved width and poor road conditions. In such cases, a larger amount of Road Width (RW) may provide drivers with more room to avoid collision with other road users or hazardous objects. On the other hand, wider road segments were found to be associated with higher accident frequencies (as given by positive sign of “RW” in Rule 3). One explanation for this is that wider road segments were located in developed areas (especially in the beginning of roadway), and thus the variable may be a representative to other risky conditions related to roadside activities such as vehicle stopping maneuvers, merging traffic from roadside, pedestrian movements along/across the road, etc. In addition, broad road widths may encourage drivers to make risky driving maneuvers, such as speeding, overtaking, and lane changing, which increase the risk of accident occurrence. This finding is consistent with that of prior studies found in the literature (Zhang and Ivan, 2005; Park et al., 2010). It is worthy to note that the RW appeared to be negatively associated with the frequency of accidents in the NLE, Poisson, and NB models (see Table 6)

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while the ANFIS model showed that RW has different effect on the accidents across the roadway; this implies that the ANFIS model could truly establish a cause-and-effect relation between road design factors and accident frequencies. The findings of this study may assist road safety authorities to reduce the likelihood and frequency of accidents by improving risky factors contributing to accident occurrence. The results indicate that the best way to do this is to manage traffic entering from minor access points, to widen very narrow road shoulders, and to develop preventive plans related to land use patterns. As discussed above, the ANFIS model suggests that the road width has different impacts on road accidents along the roadway. This implies that widening road pavement is not necessarily an effective countermeasure. However, this conclusion wasn’t extracted from the considered statistical models; particularly, those models indicated that widening road width has a positive impact on road safety. Finally, there are a few limitations to this study. First, due to unavailability of traffic data for most sections of the road, they weren’t considered in this study. Since the study area is an intercity roadway; it was assumed that most of vehicles negotiate the entire length of the road. It means that traffic flow could be nearly fixed for most parts of the road. However, the variables Land Use (LU) and Access Points (AP) may act as a surrogate to generating and attracting traffic volume on this roadway. Second, the study area was limited to 65 km segments. This may produce some problematic issues related to small sample size especially when statistical parametric models are applied to fit the data. Data characterized with small sample size can affect the estimation of the confidence intervals of model parameters and predictive performance (Xie et al., 2007; Li et al., 2008; ElBasyouny and Sayed, 2009; Park and Lord, 2009). To overcome the above-mentioned limitation, an ANFIS model was alternatively developed to handle the issue. In fact, the main reason to apply ANFIS model for this study was insufficient number of observations and covariates which increase together both uncertainty and complexity of the data. In such cases, it is difficult to develop an accurate prediction model and rational findings by using statistical approaches (Tortum, 2009). Therefore, it is the best choice to use an ANFIS model for handling the above-mentioned limitations. The results of this study have proved that ANFIS could be effective when it deals with noisy and insufficient data.

5. Conclusions This paper presented the application of ANFIS technique to estimate road accident frequencies as a function of road geometric and environmental characteristics. To do this, data on road traits and accident history were collected from a 65 km stretch of an intercity roadway connecting Qazvin to Loshan in northern Iran. Three statistical models including Poisson, negative binomial, and non-linear regression models were also developed in order to test the predictive performance of the proposed ANFIS model compared to these parametric models.

For comparison purposes, three performance criteria, including RMSE, RME, and VAF, were used (Table 7). The earlier results indicated that the variables Land Use (LU), Road Width (RW), Shoulder Width (SW), and Access Points (AP) were found to be significant on road accident frequency, while the remaining variables were found to be excluded from the model construction. The results of comparison between the ANFIS model and those three models indicated that the ANFIS model outperformed the statistical models in terms of the comparative criteria. Based on the findings of this paper, it is concluded that the proposed neuro-fuzzy model could be used as a robust and reliable approach for predicting complex and uncertain events such as road accidents, in which the combination of neural networks and fuzzy logic affords improved estimations. The ANFIS model could be an effective tool for transportation agencies since intervention decisions and plans aiming at improving road safety depend on the prediction capabilities of a system. To the best of authors’ knowledge, this is one of the first studies that has developed ANFIS technique for predicting traffic accidents and compared its results with those from conventional statistical models. Further improvements to the model may be achieved by establishing a wider database and including additional input variables related to driver behavior and road environment conditions, since these factors, notwithstanding their importance, are rarely taken into account in road safety literature.

References Abdelwahab, H. T. and Abdel-Aty, M. A. (2001). “Development of artificial neural network models to predict driver injury severity in traffic accidents at signalized intersections.” Transportation Research Record, Vol. 1746, No. 2, pp. 6-13. Adeli, H. and Karim, A. (2000). “Fuzzy-wavelet RBFNN model for freeway incident detection.” Journal of Transportation Engineering, Vol. 126, No. 6, pp. 464-471. Akgungor, A. P. and Dogan, E. (2009). “An artificial intelligent approach to traffic accident estimation: Model development and application.” Journal of Transport, Vol. 24, No. 2, pp. 135-142. Al-Ghandoor, A., Samhouri, M., Al-Hinti, I., Jaber, J., and Al-Rawashdeh, M. (2012). “Projection of future transport energy demand of Jordan using adaptive neuro-fuzzy technique.” Journal of Energy, Vol. 38, No. 1, pp. 128-135. Andrade, K., Uchida, K., and Kagaya, S. (2006). “Development of transport mode choice model by using adaptive neuro-fuzzy inference system.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 1977, Issue 1, pp. 8-16. Awad, W. H. and Janson, B. N. (1998). “Prediction models for truck accidents at freeway ramps in Washington State using regression and artificial intelligence techniques.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 1635, Issue 1, pp. 30-36. Bishop, C. M. (1995). Neural networks for pattern recognition, Oxford University Press, USA. Brijs, T., Karlis, D., Van Den Bossche, F., and Wets, G. (2007). “A Bayesian model for ranking hazardous road sites.” Journal of the Royal Statistical Society Series A: Statistics in Society, Vol. 170, Issue 4, pp. 1001-1017.

− 1770 −



Çaydaþ, U., Hasçalýk, A., and Ekici, S. (2009). “An Adaptive Neurofuzzy Inference System (ANFIS) model for wire-EDM.” Expert Systems with Applications, Vol. 36, Issue 3, pp. 6135-6139. Chiou, Y. C. (2006). “An artificial neural network-based expert system for the appraisal of two-car crash accidents.” Accident Analysis and Prevention, Vol. 38, Issue 4, pp. 777-785. Chiu, S. L. (1994). “Fuzzy model identification based on cluster estimation.” Journal of Intelligent and Fuzzy Systems, Vol. 2, Issue 3, pp. 267278. De Leur, P. and Sayed, T. (2002). “Development of a road safety risk index.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 1784, Issue 1, pp. 33-42. El-Basyouny, K. and Sayed, T. (2009). “Urban arterial accident prediction models with spatial effects.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 2102, Issue 1, pp. 27-33. El-Shafie, A., Taha, M. R. and Noureldin, A. (2007). “A neuro-fuzzy model for inflow forecasting of the Nile river at Aswan high dam.” Water Resources Management, Vol. 21, Issue 3, pp. 533-556. Greibe, P. (2003). “Accident prediction models for urban roads.” Accident Analysis and Prevention, Vol. 35, Issue 2, pp. 273-285. Hilbe, J. M. (2011). Negative binomial regression, 2nd Edition, Cambridge University Press. Ivan, J. N. and O'Mara, P. J. (1997). “Prediction of traffic accident rates using Poisson regression.” 76th Annual Meeting of the Transportation Research Board, Washington, D.C., USA Jang, J.-S. R. (1996). “Input selection for ANFIS learning.” Proceedings of the Fifth IEEE International Conference on fuzzy Systems, New Orleans, Vol. 2, pp. 1493-1499. Jang, J. S. R. (1993). “ANFIS: Adaptive-network-based fuzzy inference system.” IEEE Transactions on Systems, Man and Cybernetics, Vol. 23, Issue 3, pp. 665-685. Kim, D. G., Washington, S., and Oh, J. (2006). “Modeling crash types: New insights into the effects of covariates on crashes at rural intersections.” Journal of Transportation Engineering, Vol. 132, Issue 4, pp. 282-292. Kumara, S. S. P., Chin, H. C., and Weerakoon, W. M. S. B. (2003). “Identification of Accident Causal Factors and Prediction of Hazardousness of Intersection Approaches.” Transportation Research Record, Vol. 1840, Issue 1, pp. 116-122. Kutner, M. H., Nachtsheim, C., and Neter, J. (2004). Applied linear regression models, McGraw-Hill New, York, NY, USA. Li, X., Lord, D., Zhang, Y., and Xie, Y. (2008). “Predicting motor vehicle crashes using support vector machine models.” Accident Analysis and Prevention, Vol. 40, Issue 4, pp. 1611-1618. Lord, D., Guikema, S. D. and Geedipally, S. R. (2008). “Application of the Conway-Maxwell-Poisson generalized linear model for analyzing motor vehicle crashes.” Accident Analysis and Prevention, Vol. 40, Issue 3, pp. 1123-1134. Maher, M. J. and Summersgill, I. (1996). “A comprehensive methodology for the fitting of predictive accident models.” Accident Analysis and Prevention, Vol. 28, Issue 3, pp. 281-296. Martin, J. L. (2002). “Relationship between crash rate and hourly traffic flow on interurban motorways.” Accident Analysis and Prevention, Vol. 34, Issue 5, pp. 619-629. Miaou, S. P. and Lum, H. (1993). “Modeling vehicle accidents and highway geometric design relationships.” Accident Analysis and Prevention, Vol. 25, No. 6, pp. 689-709. Milton J. and Mannering F. (1998). “The relationship among highway geometrics, traffic-related elements and motor-vehicle accident

Vol. 17, No. 7 / November 2013

frequencies.” Journal of Transportation, Vol. 25, Issue 4, pp. 395413. Miranda-Moreno, L. F. and Fu, L. (2006). “A comparative study of alternative model structures and criteria for ranking locations for safety improvements.” Networks and Spatial Economics, Vol. 6, Issue 2, pp. 97-110. Mitra, S. and Washington, S. (2007). “On the nature of over-dispersion in motor vehicle crash prediction models.” Accident Analysis and Prevention, Vol. 39, Issue 3, pp. 459-68. Montella, A., Colantuoni, L., and Lamberti, R. (2008). “Crash prediction models for rural motorways.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 2083, Issue 1, pp. 180-189. Mousavi, S. J., Ponnambalam, K., and Karray, F. (2007). “Inferring operating rules for reservoir operations using fuzzy regression and ANFIS.” Fuzzy Sets and Systems, Vol. 158, Issue 10, pp. 1064-1082. Mucsi, K., Khan, A. M., and Ahmadi, M. (2011). “An adaptive neurofuzzy inference system for estimating the number of vehicles for queue management at signalized intersections.” Transportation Research Part C: Emerging Technologies, Vol. 19, Issue 6, pp. 1033-1047. Mussone, L., Ferrari, A., and Oneta, M. (1999). “An analysis of urban collisions using an artificial intelligence model.” Accident Analysis and Prevention, Vol. 31, Issue 6, pp. 705-718. Park, B. J. and Lord, D. (2009). “Application of finite mixture models for vehicle crash data analysis.” Accident Analysis and Prevention, Vol. 41, Issue 4, pp. 683-691. Park, B. J., Fitzpatrick, K., and Lord, D. (2010). “Evaluating the effects of freeway design elements on safety.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 2195, Issue 1, pp. 58-69. Pribyl, O. and Goulias, K. G. (2003). “Application of adaptive neurofuzzy inference system to analysis of travel behavior.” Transportation Research Record, Vol. 1854, Issue 1, pp. 180-188. Ramírez, B. A., Izquierdo, F. A., Fernández, C. G. and Méndez, A. G. (2009). “The influence of heavy goods vehicle traffic on accidents on different types of Spanish interurban roads.” Accident Analysis and Prevention, Vol. 41, Issue 1, pp. 15-24. Sangole, J. P., Patil, G. R., and Patare, P. S. (2011). “Modelling gap acceptance behavior of two-wheelers at uncontrolled intersection using neuro-fuzzy.” Procedia-Social and Behavioral Sciences, Vol. 20, pp. 927-941. Sayed, T., Abdelwahab, W., and Navin, F. (1995). “Identifying accidentprone locations using fuzzy pattern recognition.” Journal of Transportation Engineering, Vol. 121, Issue 4, pp. 352-358. Schretter, N. and Hollatz, J. (1996). “A fuzzy logic expert system for determining the required waiting period after traffic accidents.” Proceedings of the Fourth European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, pp. 2164-2170. The MathWorks Inc. (2001). Fuzzy logic toolbox user's guide, Berkeley, CA, USA. Tortum, A., Yayla, N., and Gökda go , M. (2009). “The modeling of mode choices of intercity freight transportation with the artificial neural networks and adaptive neuro-fuzzy inference system.” Expert Systems with Applications, Vol. 36, Issue 3, pp. 6199-6217. Viswanathan, M., Lee, S. H., and Yang, Y. K. (2006). Neuro-fuzzy learning for automated incident detection, Advances in Applied Artificial Intelligence, Springer Berlin Heidelberg. World Health Organization (1999). The world health report 1999: Making a difference, World Health Organization.

− 1771 −


Xie, Y., Lord, D., and Zhang, Y. (2007). “Predicting motor vehicle collisions using Bayesian neural network models: An empirical analysis.” Accident Analysis and Prevention, Vol. 39, Issue 5, pp. 922-933. Ying, L. C. and Pan, M. C. (2008). “Using adaptive network based fuzzy inference system to forecast regional electricity loads.” Energy

Conversion and Management, Vol. 49, Issue 2, pp. 205-211. Zhang, C. and Ivan, J. N. (2005). “Effects of geometric characteristics on head-on crash incidence on two-lane roads in Connecticut.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 1908, Issue 1, pp. 159-164.

− 1772 −
