1

Road Crash Frequency Prediction for Indian National Highways

using Soft-Computing Tools

Ashutosh Arun1, Erramapalli Madhu2, Senathipathi Velmurugan3

Abstract: Road crashes and road fatalities have risen quite drastically in India in the past

decade. There are several factors that affect the frequency of crashes on Indian roads ranging

from deficiencies in geometric design, poor maintenance history and other environmental and

human behavioural factors. This paper studies the effects of these factors in predicting road

crash frequency on the National Highways of India. For this purpose, crash history of 4710

crashes was collected on total segment length of 889 kilometers falling on various National

Highways in India. Additionally, data such as pavement roughness and road geometrics was

also collected. Conventional Poisson-based Generalized Linear Regression Models and

modern soft-computing methods such as Multilayer Perceptron networks and a hybrid

Adaptive Neuro-Fuzzy Inference System were configured to predict frequency of crashes.

Results indicate that the Multilayer Perceptron had the best prediction performance. A

sensitivity analysis was also subsequently performed.

Keywords: National Highways, Crash Frequency, Poisson Generalized Linear Model,

Multilayer Perceptron, Adaptive Neuro-Fuzzy Inference System

1. INTRODUCTION

Road safety has become a major issue in India. In 2013, India witnessed 486,476 road crashes

(on all types of roads) which accords it the dubious distinction of having the maximum

number of road crashes in the world (Figure 1). This is an increase of 22% compared to the

road crash numbers in the year 2001 when the widening of National Highways of India

started under the National Highways Development Project (NHDP). Also from Figure 1, we

can see that the road fatalities figure for the same year stood at 137,572. From Figure 2 it can

be seen that about 28% of these crashes and around 33% of the crash-related deaths took

place on the National Highways (NH) of India.

Figure 1: Summary statistics of road crashes in India

for the years 2001-2013. [Source: Road Accidents in

India (2013)]

Figure 2: Percentage Share of National Highways in

various statistics related to road crashes in India.

[Source: Road Accidents in India (2013)]

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Therefore, there is an urgent need to study the road crash process on Indian roads in

general and the National Highways in particular. The National Highways of India are a set of

high speed corridors linking major urban centers and other places of strategic importance in

India. For such high speed corridors, it becomes imperative to determine the contribution of

elements related to highway design and maintenance that can be controlled by engineers

towards the occurrence of road crashes so that appropriate guidelines may be evolved with a

goal to prevent future crashes and necessary corrective measures may be taken up at identified

crash prone locations.

Considering the severity of the problem, a few Indian researchers have attempted road

crash-related studies have been carried out by Indian researchers in the recent past (Dinu and

Veeraragavan, 2011). Shah (2011) developed road crash occurrence prediction models for

Indian National Highways utilizing time-series crash data collected and compiled by NHAI’s

Road Safety Cell for various national highway sections falling on Golden Quadrilateral and

North-South Corridor developed under NHDP Phase-I.

Improving upon the work done by Shah (2011), in this study the effort was made to

develop models to predict road crash frequency by considering road geometrics and pavement

roughness of the segments as well. Furthermore, it was decided to test the efficiency of soft-

computing techniques such as Artificial Neural Networks and Fuzzy Logic, which tend to

mimic human behavior and logical reasoning, towards the modeling of complex processes

such as road crashes. Thus, in this paper, Artificial Neural Networks (ANNs) and a hybrid

technique of ANN and Fuzzy Logic known as Adaptive Network-based Fuzzy Inference

System (ANFIS) were used for crash frequency prediction on Indian highways in addition to

the conventional Poisson-based Generalized Linear Regression models.

The paper has been organized in seven sections. In the next section, the literature on

modeling road crash frequency is reviewed. In Section 3, methodology adopted in the present

study is discussed. Section 4 provides the description of data used and variables considered in

the model. Section 5 discusses the details about the development of road crash frequency

prediction models and the comparison amongst the various modeling techniques. Detailed

sensitivity analysis is presented in Section 6. Finally, Section 7 gives the conclusions drawn

from the study.

2. LITERATURE REVIEW

Theoretically, crash frequency variable can be considered as being Poisson distributed (Lord

et al., 2005). Miaou (1994), Vogt and Bared (1998) and Kononov and Allery (2003) have

demonstrated the successful use of Poisson and Negative Binomial (NB) regression in

modeling crash frequency. Importantly, in Thailand, where the roads operate under mixed

traffic conditions like in India, Poisson and NB-based Crash Prediction Models have been

successfully deployed (Thailand Accident Research Centre, 2009).

However, the Poisson Generalized Linear Model suffers a few drawbacks. Due to the

Poisson property where the variance is constrained to be equal to the mean, the Poisson

distribution cannot handle over- or under-dispersion. In order to overcome this shortcoming, a

robust covariance estimator (also known as Huber/White/Sandwich estimator) can be used to

estimate the coefficients of the Poisson model (Freedman, 2006; Hilbe, 2007). It is called

“robust” because it provides consistent estimate of variance of the Maximum Likelihood

estimates even when the underlying model specification is wrong.

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The Poisson models are still fraught with several other shortcomings as explained by

Lord and Mannering (2010). More importantly, with regard to its specific application in India,

Dinu and Veeraragavan (2011) have strongly criticized the fixed parameters assumption of

Poisson models as they feel that it cannot suitably capture the huge variability arising out of

heterogeneous traffic conditions and other social and environmental factors prevalent here.

In view of such drawbacks of conventional models, several authors have also sought

to apply soft-computing methods such as Artificial Neural Networks and Fuzzy Logic models

for the purpose of crash prediction. These soft-computing tools have been proved to be

universal approximators (Cybenko, 1989; Stinchcombe and White, 1989; Kosko, 1992). The

most popular Feed-Forward ANN in crash prediction is Multilayer Perceptron (MLP)

network. Pande and Abdel-Aty (2006) demonstrated the applicability MLP for crash

frequency prediction. Xie et al. (2007) and Cansiz and Easa (2011) showed that the ANN

models provided superior results to the conventional stochastic models.

Adaptive Neuro-Fuzzy Inference System (ANFIS), originally developed by Jang

(1993), is a hybrid of the ANN and Fuzzy Logic techniques. It utilizes feed-forward neural

networks with supervised learning to tune a Sugeno-type Fuzzy Inference System and hence

combines the advantages of both the techniques. For this reason it has been used for crash

frequency prediction by some researchers (Awad and Janson, 1998; Zheng and Meng, 2011).

Indeed it needs to be mentioned that the soft-computing techniques are also plagued by

disadvantages such as over-fitting of the training data, ‘black-box’ nature, the “curse of

dimensionality” (Bishop, 1995; Friedman, 1997) etc.

3. METHODOLOGY

For the present study, a road crash was defined as a collision occurring between two or more

objects on a road section, at least one of which is any type of a moving vehicle.

The crash data were collected from the Road Safety Cell of National Highway

Authority of India (NHAI) for select stretches and these were then collated and merged with

quantitative road geometry and pavement roughness data collected using the Network Survey

Vehicle (NSV) of CSIR-Central Road Research Institute (CSIR-CRRI). The preliminary

database so created was then subjected to data pruning. Thereafter, the final variables for

modeling were selected and checked for the presence of correlations. These variables were

subjected to exploratory data analysis to identify patterns present in the data and to formulate

hypotheses regarding the individual dependent-independent variable relationships. Finally the

following models were prepared to predict crash frequency:

Poisson Generalized Linear Model

Multilayer Perceptron (MLP) Model

Adaptive Neuro-Fuzzy Inference System (ANFIS) Model

Before the estimation of the Poisson model, as is the vogue, the data was tested for the

presence of over- or under- dispersion using the following tests:

Regression-based tests calculating a dispersion statistic using Deviance and

Pearson’s chi-square

Lagrange Multiplier (LM) test (for details refer Cameron and Trivedi, 1998)

If dispersion was found, it was proposed to use the Quasi-Maximum Likelihood

Estimation and/or the Robust Covariance Estimator approach to handle the dispersion. The

models so developed were then compared with each other based on the error measures such as

Mean Absolute Error (MAE) and Root-Mean Squared Error (RMSE).

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Additionally, sensitivity analysis was carried out using finally selected model/s to find

out the relationship of individual variables with crash frequency.

4. DATA AND VARIABLES

4.1 Data Collection and Collation

The crash data for the year of 2012 were collected from the Road Safety Cell of National

Highway Authority of India (NHAI) for select stretches on 8 National Highway corridors

geographically distributed across the country. These sections were recently widened to four

lane divided carriageways under NHDP Phase-I and fall on the important Golden

Quadrilateral (GQ) Corridor that connects the four major metropolitan cities of India namely

Delhi, Mumbai, Chennai and Kolkata. Only segment crashes were considered under this

study. The study sections are indicated in Figure 3.

Figure 3. Map of Golden Quadrilateral Project under NHDP Phase-I. [Source:

http://nhai.org/gqmain_english.htm] [Note: Entire GQ stretch is shown with study sections marked in bold lines

and labeled]

The crash data that were collected contained information regarding the day and time of

crash, crash location in terms of chainages, weather condition at the time of crash, cause/s of

crash (such as over-speeding, drunken driving etc.), nature of crash (i.e. overturning, head-on

collision, rear-end collision etc.), severity outcome of the crash etc. Quantitative road

geometry data (vertical gradient and horizontal curvature) and information regarding

pavement surface condition in terms of the International Roughness Index (IRI) were

collected for the study sections using the Automatic Road Survey System of CSIR-Central

Road Research Institute. The road geometry data were then integrated with the crash data

created earlier to create a preliminary database.

While collating the data, it was observed that the entries regarding exact crash location

for crashes on NH 2 were incomplete and hence the data for NH 2 were not entered into the

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database. After removing the missing values, repeated observations and cases for which the

information seemed dubious, the database had records for 4710 crashes occurring on 889

homogeneous sections (based on traffic volume and horizontal and vertical alignment) along

with the road geometry and IRI data for all the study sections.

4.2 Variable Selection

Consistent with the objective of the paper wherein it was sought to model the effect of the

environmental and behavioral factors in addition to the engineering ones on crash frequency,

the following variables were selected for the modelling purpose as given in Table 1.

Table 1. List of Model Variables

S. No. Name of the Variable Name of the

Variable in the

Model

Nature of the

Variable

Variable Function in

the Model

1 Average Daily Traffic - - Multiplicative

Constant

1 Time of the Day Time Categorical Explanatory

2 Weather at the time of Crash Weather Categorical

3 Causal Conditions CC Categorical

4 Pavement Roughness (in IRI) IRI Continuous

5 Horizontal Curvature (in deg/km) Curve Continuous

6 Vertical Gradient (in %) Grade Continuous

7 Annual Crash Frequency Frequency Continuous Response

As seen in Table 1, logarithm of the Average Daily Traffic was used as the measure of

traffic exposure only and was multiplied with the result of the model in order to obtain the

final frequency values. The selected model variables were thereafter checked for correlations.

No significant correlations among the variables were found, as shown in Table 2.

Table 2. Spearman’s Rank-Correlation Coefficients for Independent Variables

TC WC CC Avg. Grade Avg. Curve Avg. IRI

TC 1.000

WC -0.003 1.000

CC -0.049 0.035 1.000

Avg. Grade -0.005 -0.024 -0.041 1.000

Avg. Curve 0.050 0.066 -0.019 -0.061 1.000

Avg. IRI -0.037 0.041 -0.067 0.056 0.112 1.000

Tables 3 and 4 provide details about the categorical variables and summary statistics

for the continuous variables respectively for providing deeper insights into the data.

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Table 3: Details of Categorical Variables

Categorical

Variable

Categories Coding

Information

Crash

Counts

Percentage share in

total crashes

Time of Day 22 – 2 hrs. Time=1 438 9.30%

2 – 6 hrs. Time=2 897 19.04%

6 – 10 hrs. Time=3 810 17.20%

10 – 14 hrs. Time=4 769 16.33%

14 – 18 hrs. Time=5 777 16.50%

18 – 22 hrs. Time=6 524 11.13%

Unknown Time=7 495 10.51%

Weather

Condition

Fine Weather=1 3608 76.6%

Extreme Temperatures Weather=2 483 10.25%

Bad Weather with Low Visibility Weather=3 456 9.68%

Very Bad Weather with Very Poor

Visibility

Weather=4 102 2.17%

Unknown Weather=5 61 1.3%

Causal

Condition

Drunken Driving CC=1 137 2.91%

Over-speeding CC=2 3116 66.16%

Vehicle out of control CC=3 660 14.01%

Fault of driver or other road user CC=4 640 13.59%

Mechanical defect in vehicle/ Poor

road condition

CC=5 147 3.12%

Unknown CC=6 10 0.21%

Table 4: Summary Statistics for Continuous Variables

Average

Daily Traffic

(in PCU)

Avg. IRI (in

m/km)

Avg. Grade (in

%)

Avg. Curve (in

deg/km)

Crash

Frequency

Mean 34477 2.85 0.019 38.13 0.026

Median 29411 2.68 -0.007 30.65 0

Standard

Deviation

17378 0.77 1.02 28.68 0.169

Sample

Variance

0.59 1.04 822.38 0.029

Minimum 16934 1.505 -7.87 6.11 0

Maximum 64409 7.417 5.16 237.92 8

It can be seen from Table 4 that the Crash Frequency variable seems almost equi-

dispersed. However, before final model development, a formal test was proposed to be carried

out to ascertain the presence (or absence) of any over-dispersion whatsoever. After this the

final analysis was performed using the Poisson Generalized Linear Regression as a

conventional modelling tool followed by the configuration of soft-computing models.

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5. MODEL DEVELOPMENT

It was sought to carry out external validation in addition to the usual internal validation for

testing the reproducibility of model results as suggested by Justice et al. (1999). For this

purpose, data for one highway corridor i.e. NH 79A & 79 was set aside from model

development and used exclusively for the purpose of external validation. The rest of the data

were divided in a ratio of approximately 70:30 to obtain the calibration and internal validation

datasets. The following sub-sections give the details of the models developed on the

calibration set.

5.1 Poisson Generalized Linear Models

The Poisson Models were fitted using the GENLIN command in SPSS® software. Log was

used as the link function for all the Poisson models that were developed. A hybrid method for

ML estimation was adopted where 1 iteration of Fisher’s scoring method was first employed

followed by Newton-Raphson method for faster convergence. Several Poisson models were

estimated incorporating the main effects and/or the various interactions of the independent

variables.

A LM test was conducted to check for the presence of over-dispersion. Also, it was

found that though the complete dataset indicated possible presence of over-dispersion, if one

utilized only a part of the dataset for modeling purpose, the data started showing signs of

equi-dispersion and sometimes even under-dispersion. This was also a problem observed by

Daniels et al. (2010). Cameron and Trivedi (1998) have also cautioned that an apparent over-

dispersion in the data might get eliminated once we include regressors in the model.

Thus, for the LM test, a NB log-linear model with its dispersion parameter set to 0 was

calibrated on the calibration dataset and the null hypothesis that the dispersion parameter

value is 0 was tested. The results (Table 5) indicated that under-dispersion was significant at

5% level of significance (p-value = 0.017). However, even non-directional dispersion was

significant at this level of significance. Moreover, the null hypothesis could not be rejected if

the results were considered at 1% level of significance indicating that nothing could be said

conclusively.

Table 5: Lagrange Multiplier test results

LM test

statistic

p-values (by Alternative Hypothesis)

Dispersion Parameter <

0

Dispersion Parameter >

0

Dispersion Parameter ≠

0

Ancillary

Parameter

-2.124 0.017 0.983 0.034

Thus in order to obtain conclusive evidence regarding the absence of under-dispersion

the dispersion statistics using Deviance and Pearson’s chi-square were also calculated (Table

6). Table 6. Dispersion statistic calculated from Deviance and Pearson’s chi-square

Value df ϕ̂

Deviance 12082.2 108133 0.112

Pearson Chi-Square 107827.1 108133 0.997

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As it can be seen from Table 6, while the dispersion statistic from deviance indicated

under-dispersion, the one derived from Pearson’s chi-square has a value very close to 1,

indicating that data may be safely assumed to be equi-dispersed. It has been suggested in

literature that Pearson’s chi-square-based scaling should be preferred over Deviance-based

scaling (Hilbe, 2007; Barros and Hirakata, 2003). So it can be concluded that un-scaled

Poisson models could have been developed. Nevertheless, robust estimators for covariance

matrix were used in estimation just to be on the safer-side.

It was found that the various models with interaction terms were either found to be

showing lesser fit than the main effects-only model or found to be affected by

multicollinearity. Hence, finally the main effects-only model was chosen. Table 7 gives the

coefficients obtained using the Poisson regression. It can be seen that except the variable

Time=6, which corresponds with a time period of 6 PM to 10 PM, rest all of the variables

have proved to be significant predictors of road crash frequency variable.

Table 7: Parameter Estimates for Poisson model

Parameter β t-statistic

(Intercept) -10.631 -24.205

Time=1 -.254 -3.144

Time=2 .353 5.389

Time=3 .356 5.362

Time=4 .353 5.222

Time=5 .330 4.889

Time=6 .024 0.327

Time=7 0

Weather=1 3.770 25.681

Weather=2 1.648 10.338

Weather=3 1.827 11.644

Weather=4 .416 2.218

Weather=5 0

CC=1 2.502 5.896

CC=2 5.720 14.002

CC=3 4.100 9.968

CC=4 3.955 9.601

CC=5 2.842 6.771

CC=6 0

IRI -.064 -2.723

Grade .068 4.503

Curve .004 8

Log-Likelihood Ratio

(LL0/ LLβ) -8869.958

McFadden’s R2

(1- LLβ/LL0) 0.9

From the Table 7 above, it can be seen that the McFadden’s pseudo-R squared

measure, which is a statistic indicating the goodness of fit of the model, is over 0.9 indicating

that the developed model fits the data perfectly. The developed model was tested for the

presence of heteroscedasticity by plotting the Standardized Deviance Residuals against the

model predicted results. Given that on visual inspection, the model showed signs of

heteroscedasticity (Figure 4) it seems that the robust variance estimators proved to be a good

choice for model development.

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Figure 4: Visual Inspection for Heteroscedasticity

5.2 Multilayer Perceptron Models

The MLP model contained 21 input nodes and one output node. Based on literature review, it

was decided that one hidden layer would be sufficient in the model. The optimal number of

neurons in the hidden layer was estimated based on a cross-validation technique. The MLP

models were fitted using the MLP command in SPSS.

Scaled Conjugate Gradient (SCG) Algorithm with batch training was used for training

the network as it is faster and more efficient than standard Back-Propagation Algorithm

(Moller, 1993). The default values were used for the parameters in SCG algorithm. Sum of

squares was used as the error function. The maximum number of training epochs was limited

to 1000.

Several model runs with different rescaling options (standardization, normalization

and adjusted normalization) for both input and output continuous variables, different

activation functions (hyperbolic tangent and sigmoid for hidden layer and hyperbolic tangent,

sigmoid, identity and softmax for output layer) and with different random seeds (leading to

different initial settings like initial weight matrices, initial automatic architecture selections

etc.) were done. Any other settings were kept at their default values. The best performing

network produced had 9 hidden neurons and was obtained at the following settings:

Covariates rescaled using standardization; the dependent variable rescaled using

normalization.

Sigmoid activation function in both hidden and output layers

5.3 Adaptive Neuro-Fuzzy Inference System Models

The ANFIS models were developed using MATLAB® Fuzzy Logic Toolbox. The Fuzzy

Logic Toolbox gives three options for configuring an initial Sugeno-type FIS in the form of

grid partitioning, subtractive clustering and fuzzy c-means clustering. Since grid partitioning

suffers from the “curse of dimensionality”, the choice was limited to the clustering

techniques. Hammouda and Karray (2000) compared the two clustering techniques and found

that fuzzy c-means clustering performed better in terms of lower RMSE values, higher

classification accuracy and lower computation time required. Thus, it was decided to use

fuzzy c-means clustering to generate an initial FIS.

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This was accomplished by using the genfis3 function of the Fuzzy Logic Toolbox

which uses the fcm function (fuzzy c-means clustering) to determine the number of rules and

membership functions for the premise and consequents. By default, the premise membership

functions are Gaussian “bell-shaped” functions and the consequent membership functions are

linear. A problem with fcm is that it is sensitive to the initial conditions and hence several runs

were done to decide upon the best performing FIS (The best performing FIS is one that

produces the minimum value of an objective function). However, the different runs did not

produce any significant improvement in performance in our case. For each run, the default

fcm options were maintained.

The objective of applying the adaptive network to this initial FIS is to tune the

parameters of the membership functions so that the overall RMSE is minimized. Thus, to tune

the network the anfis function of the Fuzzy Logic Toolbox was used. The default options for

this function were kept as it is.

While developing the initial FIS structure for ANFIS models, initially the ‘auto’

option in fcm function was used where it utilizes a subtractive clustering technique to find out

the number of clusters. However, this strategy was found to be computationally very

expensive. Hence the number of clusters was found alternatively by starting with an initial of

5 clusters and then increasing them in steps of 5. The tuning of initial FIS using anfis function

was also done for each number of clusters in order to gauge the effect of increasing the

number of clusters on training time requirement.

The FIS obtained by this method was thus limited to 10 rules. Thus, the final ANFIS

network had 10 Gaussian membership functions for each of the 21 inputs, and 10 linear

membership functions for the output. The maximum number of training epochs was limited to

10 as an increase in the number of training epochs also increased the training time

requirement manifold.

6. RESULTS

Table 8 gives the error measures for all the three models in all the three phases: calibration,

internal validation and external validation, and also overall.

Table 8. Comparison of models based on error statistics

Model Calibration Internal Validation External Validation

MAE RMSE MAE RMSE MAE RMSE

Poisson 0.04 0.15 0.04 0.15 0.04 0.17

MLP 0.03 0.12 0.01 0.08 0.01 0.06

ANFIS 0.05 0.15 0.04 0.17 0.05 0.16

It can be seen from Table 8 that the Poisson and ANFIS models show almost similar

results. The MLP results are however better than the other two models, more so when we take

the validation results in comparison. This proves that the repeatability and reproducibility of

MLP model results are the best amongst all the models tested. Also, the MLP model had a

lower training time requirement when compared to the ANFIS model which makes it a more

attractive method. Thus, on the basis of the following results, the MLP models can be

regarded as the most suitable tool for modeling crash frequency for Indian national highways.

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7. SENSITIVITY ANALYSIS

Before proceeding with the sensitivity analysis for individual variables, an attempt was made

to determine the relative importance of each variable towards predicting a road crash. The

MLP command in SPSS provides an option of conducting the importance analysis. The

results of this analysis are provided in Table 9.

Table 9. Importance Analysis for Independent Variables

Variables Importance

Time .076

Weather .293

Causal Conditions .345

Grade .133

Curve .153

IRI .086

From Table 9, it can be seen that the weather conditions and causal conditions possess

a high influence in predicting road crash frequency.

For sensitivity analysis, both Poisson GLM and MLP models were employed.

However, it was observed that the variable relationships derived using the Poisson model did

not agree with the observed behavior of factors. Thus, only the MLP model results are

presented below.

In the process of sensitivity analysis, firstly only the levels of categorical variables

were varied while keeping the continuous variables fixed at their mean values. The predicted

mean values were then averaged for a particular category of a particular variable and

presented in Figure 7.

0.007

0.0290.024

0.0220.024

0.010

0.000

0.010

0.020

0.030

0.040

22-2 hrs. 2-6 hrs. 6-10 hrs. 10-14 hrs. 14-18 hrs. 18-22 hrs.

Mar

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Time of Day

0.107

0.002 0.008-0.007

-0.0200.0000.0200.0400.0600.0800.1000.120

Fine ExtremeTemperatures

Bad Weatherwith PoorVisibility

Very BadWeather with

Very PoorVisibility

Mar

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Weather Conditions

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Figure 5: Sensitivity Analysis for categorical variables

From Figure 5, the following inferences can be drawn:

Amongst all the categorical variables, causal conditions especially over-speeding

have the maximum positive effect on crash frequency highlighting the role of

human factors in crash causation.

The marginal crash frequency (MCF) values for the daytime hours are 0.024,

0.022 and 0.024. Thus, compared to night-time categories, the day-time actually

contributes more towards crash counts. The MCF value is the highest (0.029) for

the 2 AM – 6 AM time period category.

Fine weather conditions are proved to be conducive to higher crash frequencies as

the MCF value (0.102) is higher by a large margin when compared to the other

weather conditions defined in the database. Possible reckless driving and higher

speeds may be the reason behind this. The minimum effect is of the most adverse

weather condition of “Very bad weather with very poor visibility” perhaps due to

rarity of observing this weather condition in field.

An interesting point to note is that though the number of crashes observed were

more under Extreme Temperature Conditions (Weather = 2), the MCF is higher

for lightly inclement weather conditions indicated by the third category. Thus,

other conditions remaining constant, weather conditions such as light rain/strong

winds/light dust storms etc. shall result in more crashes than very high/very low

temperature conditions.

In the second step of sensitivity analysis, the continuous variables were varied one-by-

one within a range for which a large number of cases were observed in the database while the

other continuous variables were kept at their average values. This was repeated for all the

values of the continuous variables to get expected values for marginal crash frequency. The

results are presented in Figure 6.

-0.005

0.113

0.0180.013 -0.007

-0.0200.0000.0200.0400.0600.0800.1000.120

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Causal Conditions

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Figure 61: Sensitivity Analysis for continuous variables

Some inferences drawn from the Figure 6 are as below:

For average Gradient variable the marginal crash frequency is expected to show a

very small increase from 0.009 to around 0.012 as the gradient changes from -7%

to +7%.

The relationship between marginal crash frequency and average curvature is

monotonically non-decreasing. Thus, lower the curvature, lower the crash

frequency.

The relationship between marginal crash frequency and average curvature is

monotonically non-decreasing i.e. greater the IRI, lesser the marginal frequency

8. CONCLUSION

The road crash frequency prediction models for Indian National Highways were developed in

this paper. An important objective of this paper was to compare the suitability of application

of soft-computing tools such as Artificial Neural Networks and Fuzzy Logic for the purpose

of prediction of crash frequency on Indian national highways. In that sense, it can be safely

declared that the ANN, particularly the Multilayer Perceptron (MLP) model, is a successful

technique as it has a performance better than the conventional crash frequency modeling

methods such as Poisson GLM. In fact, if one takes into account the insight that MLP model

enables one to have in the individual independent-dependent variable relationships, it will be

justified to say that MLP even outperforms the conventional modeling methods.

The sensitivity analysis done with the help of MLP models revealed that the human

and vehicle-related causal conditions are the main determinants of crashes occurring on

Indian highways. The road geometry has far lesser impact on crash causation. So it can be

argued that engineering solutions alone cannot have a very significant mitigating effect on

0

0.005

0.01

0.015

0.02

0.025

-8 -6 -4 -2 0 2 4 6 8

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ncy

Avg. Gradient (in %)

0

0.02

0.04

0.06

0.08

0 200 400

Mar

gin

al C

rash

Fr

eq

ue

ncy

Avg. Curvature (in deg./km)

0

0.005

0.01

0.015

0.02

0.025

0.03

0 5 10

Mar

gin

al C

rash

Fr

eq

ue

ncy

Average IRI (in m/km)

14

road crashes. The other two E’s of road safety i.e. Education and Enforcement will have to

play a far greater role in order to achieve any drastic results.

There are certain limitations of the study as well:

Speed is an important determinant of road crashes but since the data regarding the

vehicular speeds at the time of crashes was not readily available it could not be

utilized for modeling purpose.

Since all the highways considered in the study were four-lane divided highways, the

scope of the models is limited to this category of highways only.

Temporal and Spatial correlations, if present, were ignored in the study due to

incompleteness of the database.

ACKNOWLEDGEMENT

We are very grateful to the Director, CSIR-Central Road Research Institute for allowing us to

publish this paper.

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