Modeling the Perception Reaction Time and

Modeling the Perception Reaction Time and Deceleration Level for Different Surface Conditions using Machine Learning Techniques Mohammed Elhenawy1, Ihab El-Shawarby1,2, Hesham Rakha1,3 ∗ 1

Virginia Tech Transportation Institute, Blacksburg, USA Faculty of Engineering, Ain-Shams University, Cairo, Egypt 3 Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, USA 2

Abstract. The ability to model the driver’s perception reaction time (PRT) and deceleration level is important for signal-timing design. The current state of practice considers PRT and the deceleration level deterministic and uses of constant values for them. The state of practice ignores the differences in PRT and deceleration level between individual drivers approaching the same intersection at the onset of yellow. The research presented in this paper uses data collected from two controlled field experiments on the Smart Road at the Virginia Tech Transportation Institute (VTTI) to model brake PRT and the deceleration level at the onset of a yellow indication for different roadway surface conditions. The paper uses many of the recent stat of art machine learning to train models that can be used to predict the brake PRT and deceleration level of approaching driver. Keywords: Brake Perception Reaction Time · Deceleration · Machine Learning · Deep learning.

1

Introduction

With advances in sensing, communications, and computational technologies, research in the area of safety is increasing significantly. Most new cars have active safety features including anti-lock braking and adaptive cruise control systems to reduce road accidents [1]. In the US, the Department of Transportation (DOT) reported 32,367 fatalities caused by road accidents in 2011 [2]. A significant percentage of these road accidents occurred at signalized intersections because of the dilemma zone problem. Rear-end crash and right-angle crash are the two types of dilemma-zone-related crashes. These crashes can be avoided if the yellow time is properly designed. Driver perception reaction time (PRT) is important in the calculation of the yellow interval duration in traffic signal design [3]. So that an accurate estimation of the PRT is required for a proper design of the yellow time. PRT is a random variable, which has a

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distribution, and the state of practice in designing the yellow time uses the 85th percentile brake PRT that equals 1.0-s [4]. However, there are studies showed that the brake PRTs lies in the range of 1.1 to 1.3 s [5]. PRT is the sum of two portions. The first is the time a driver needs to perceive sensory signal and decide his response. The second portion is the time needed for executing the decided response. For example, the PRT of a driver at the onset a yellow light at a traffic signal consists of the time needed to perceive the yellow light and decide to stop plus the time needed to move his foot from the accelerator and touching the brake [6]. In general, PRT studies can be classified into three categories: simulator studies, controlled road studies, and naturalistic observation [6]. Each study type has limitations that we need to consider when generalizing its outcome to normal driving conditions. The drivers in simulator and controlled road are more alert than under normal driving conditions which may yield shorter PRT measurements. Naturalistic studies have the highest validity, however it is not possible to test effects of independent variables, place drivers in emergency or even urgent situations, measure perception and movement times separately, or control driver demographics to avoid sample bias. Caird, et al. conducted a simulator study which included 77 drivers approaching signalized intersections at 70 km/h. The analysis of the driver’s behavior showed that the PRT is significantly affected by the time to intersection (TTI) but not the age. Moreover, they demonstrated that PRT has a grand mean of 0.96 s and ranges from 0.86 s for drivers closest to the intersection stop line to 1.03 s for drivers farthest from it. In another study [7]. Rakha., et al. conducted a controlled road study where data was collected from 60 participants to study driver brake PRTs at the onset of the yellow indication at high-speed signalized intersection [8]. The study demonstrated that the distribution of the brake PRT could be modeled using lognormal or beta distribution. They show that the state of practice 1.0-s, 85th percentile PRT used in the design of traffic signals is valid. El-Shawarby, et al. conducted controlled a road study to characterizes the impact of a wet road surface and rainy weather conditions on driver PRT at the onset of the yellow indication on the approach to a high-speed signalized intersection [9]. The study demonstrated that driver PRT increased under conditions of a wet pavement surface and rainy weather as compared to clear weather conditions over the entire TTI range. Transportation engineers consider driver deceleration levels in the design of yellow time as well. Traffic signal designers assumed constant driver deceleration levels equal 3 m/s2 or 10 ft/s2. Moreover, driver deceleration levels are important in most traffic simulators, vehicle fuel consumption and emission models, and design of deceleration lane lengths. Many studies done to characterize the mean and range of the deceleration level and what factors affect it. An early study conducted at Connecticut demonstrated that the average maximum brake deceleration level was 0.95 m/s2 (9.7 ft/s2) for vehicles moving at speed 16.1 to 40.2 km/h (10 to 25 mph) [10]. Parsonson and Santiago studied 54 intersection approaches in four counties in the southeastern United States and concluded that 3 m/s2 (10 ft/s2) is a good estimate for the brake deceleration level [11]. Two other research effort were done at different intersections in metropolitan areas in Phoenix, Arizona, and Tucson, Arizona [12], [13] to find out the mean deceleration level at higher speeds. Both studies reported wide interval of deceleration level with upper bound

greater than or equal 4 m/s2 (13.2 ft/s2). El-Shawarby, et al. conducted a controlled field test to study the impact of several factors such as age, gender, and TTI on driver deceleration levels at the onset of the yellow indication on high-speed signalized intersection approaches [14]. This study showed that the mean deceleration level ranges from 3.6 to 4.1 m/s2 which is significantly higher than the 3 m/s2 deceleration level used in the state-of-the-practice traffic signal design guidelines. Moreover, the results demonstrate that at shorter TTIs at the onset of yellow the driver deceleration levels are higher. Furthermore, deceleration levels of older drivers (60 years of age or older) are greater than deceleration levels of younger (under 40 years old) and middle-aged (between 40 and 59 years old) drivers. The deceleration level at stop-controlled intersections grabbed the attention of the researchers as well. Wang et al. recommended a maximum deceleration level of 3.4 m/s2 (11.2 ft/s2) for passenger cars approaching stop-controlled intersection. They reported that the 3.4 m/s2 (11.2 ft/s2) was corresponding to the 92.5th percentile deceleration level at stop-controlled intersections [15]. Another research done at rural stop sign–controlled intersections in southern Michigan to study the factors explaining the variation in the observed deceleration and acceleration rates. The study concluded that the initial speed, driver demographics, and time of day explained about 18% , 5% and 5% of the variation in deceleration levels respectively [16]. The past two decades have seen numerous research efforts and advances in both machine learning and computers. Many machine learning techniques require a large number of computations and are infeasible without computers. The available machine learning algorithms and computation power encourages researchers to transfer this knowledge into their fields. Transportation engineers are among people who are interested in applying these algorithms to address transportation problems. This interest increases with the availability of naturalized data sets and data sets collected from controlled experiments. Recently, some machine learning algorithms were used in the transportation field, including: classifying and counting vehicles detected by multiple inductive loop detectors [17], identifying motorway rear-end crash risks using disaggregate data [18], automatic traffic incident detection [19], real-time detection of driver distraction [20, 21], transportation mode recognition using smartphone sensor data [22], and video-based highway asset segmentation and recognition [23]. Modeling driver stop/run behavior at signalized intersections is very important and is ideal for applying machine learning techniques [24],[25]. The modeling of brake PRT and declaration levels seems to be a good candidate for application of machine learning algorithms. Observations of the stopping driver from naturalized datasets or from controlled field experiments, datasets can be used to train machine learning algorithms. The trained models could then be used to predict future driver brake PRT time and deceleration level at the onset of yellow light. In this paper, we adopted the state of art machine learning techniques to model the brake PRT and deceleration levels of the driver at the onset of the yellow signal. We demonstrate that models built using machine learning algorithms give better prediction than the traditional multiple linear regression.

2

Methods

In this section, we briefly describe the feature selection algorithm and the classifiers used in this paper as building blocks in the proposed hierarchal classifier. 2.1

Decision Tree

Decision tree method is a greedy and recursive algorithm starts from a root where the entire data is in one node. Subsequently, a tree is grown by splitting the data using binary splitting approach. The chunk of the data at the parent node is portioned between the resultant leaves to minimize the objective function. In order to predict the response for a new unseen test observation, it pushed down by going through the tree from the root to a leaf. The final leaf determines the response of the test observation [26]. While growing the tree, the data is divided by employing a criterion in several steps or nodes. In practice, Gini index, and Cross-Entropy are used for classification and mean-square error (MSE) of the responses is used for regression. 2.2

Random Forest

Random forest method, as proposed in 2001 [27], creates an ensemble of decision trees. For each tree, a subset of features is randomly selected to grow the tree. Also, adding more trees does not lead to over-fitting but at some point not much benefit is gained by including more trees [28]. The response of a test observation is obtained by averaging the predictions from all the individual regression trees on this unseen test observation. 2.3

Adaptive Boosting Algorithm

The Adaptive Boosting (AdaBoost) is a machine learning algorithm that is based on the idea of incremental contribution [29].AdaBoost was introduced as an answer to the question of whether a group of “weak” learner algorithms that each has low accuracy can be grouped together and boosted into an arbitrarily accurate “strong” learning algorithm. In this paper we used the LSBoost (least squares boosting) which fits regression tree ensembles. LSBoost minimizes the mean-squared error, at each iteration, by adding a new-trained tree. The algorithm fits a new tree to the difference between the observed response and the ensemble prediction, which includes all trees trained in the previous iterations. 2.4

Artificial neural networks

In machine learning, artificial neural networks (ANN) are used to estimate or approximate unknown linear and non-linear functions that depend on a large number of inputs. Artificial neural networks can compute values or return labels using inputs. An ANN consists of several processing units, called neurons, which are arranged in layers. ANN can uses learning algorithm such as back propagation to learn the weights and biases for each single neuron[30]. This kind of network its perfor-

mance get worse as the number of hidden layers increases because of the vanishing of the gradient. In this paper we used the autoencoder which is proposed by Hinton and Salakhutdinov [31] to build deep network. An autoencoder can discover interesting structure in the data by setting its inputs and outputs equal and using backpropagation to learn its weights and biases.

3

Data Description

The data used in this paper was collected from two different field experiments. The field experiments done at the Virginia Department of Transportation’s (VDOT) Smart Road facility, located at the Virginia Tech Transportation Institute (VTTI). The length of the Smart Road is a 3.5 km (2.2 mile). It is a two-lane road with one four-way signalized intersection. The horizontal layout of the test section is fairly straight, and the vertical layout has a substantial grade of 3% [32]. The two field data collection efforts were conducted to characterize driver behavior at the onset of a yellow indication as a function of various driver and traffic stream characteristics under different weather conditions. Two vehicles were used in each study, one was driven by test participant (accompanied by the in-vehicle experimenter) and the other vehicle was driven by a trained research assistant to simulate real-world conditions by crossing the intersection from the side street when the signal was red for the test vehicle. The test vehicle was equipped with a real-time data acquisition system (DAS), differential Global Positioning System (GPS) unit, a longitudinal accelerometer, sensors for accelerator position and brake application, and a computer to run the different experimental scenarios. The vehicle data stream was synchronized with changes in the traffic signal controller by the communication channel that links the data recording equipment to the intersection signal control box. The phase changes was triggered by the test vehicle using the GPS unit to determine the distance from the intersection. The two vehicles were equipped with a communications system between them, operated by the research assistants, and with the Smart Road control room. In both studies, participants drove loops on the Smart Road, crossing a four-way signalized intersection where the data were collected. Exclusive of practice trials, the participant drove the entire test course 24 times for a total of 48 trials, where a trial consists of one approach to the intersection. Each participant was tested individually. Among the 48 trials, there were 24 trials in which each yellow trigger time to stopline occurred four times. For the remaining 24 trials, the signal indication remained green. 3.1

Dry roadway surface field experiment

In this study, twenty-four licensed drivers were recruited in three equal age groups (under 40-years-old, 40 to 59-years-old, and 60-years-old or older); equal number of male and female participants were assigned to each group [33]. The data collection effort was conducted under clear weather conditions. The test conditions were based on two instructed vehicle speeds of 72.4 km/h (45 mi/h) and 88.5 km/h (55 mi/h). Each participant was assigned to the two test conditions (sessions), one test condition

per day, taking approximately 1.5 hours per session to complete. A 4-second yellow interval at the 72.4 km/h instructed speed and a 4.5-second yellow interval at the 88.5 km/h instructed speed were triggered for a total of 24 times (four repetitions at six distances). The yellow indications were triggered when the front of the test vehicle was 40.2, 54.3, 62.5, 70.4, 76.5, and 82.6 m (132, 178, 205, 231, 251, and 271 ft) from the intersection for the 72.4 km/h instructed speed and 56.7, 76.2, 86, 93.6, 101, and 113 m (186, 250, 282, 307, 331, and 371 ft) for the 88.5 km/h instructed speed. 3.2

Rainy/wet roadway surface field experiment

In this study, twenty-six drivers were recruited in three age groups (under 40-yearsold, 40 to 59-years-old, and 60 years of age or older), each group is male-female balanced [34]. The major differences of this study than the previous one were: (a) all runs were conducted under rainy weather conditions with wet pavement surfaces and (b) all runs were executed at only one instructed speed of 72.4 km/h (45 mi/h). A 4second yellow interval at the 72.4 km/h instructed speed was triggered for a total of 24 times (four repetitions at six distances). The yellow indications were triggered when the front of the test vehicle was 54.3, 62.5, 70.4, 76.5, 82.6, and 92.7 m (178, 205, 231, 251, 271, and 304 ft).

4

Results

This section presents the regression results of the machine learning algorithms. There are six predictors used to predict the PRT and deceleration level of the driver: Ge is the gender (1 = female, 0 = male) Gr is the grade (1 = downhill, 0 = uphill) A is the age (years) TTI is the time-to-intersection V is the approach speed (km/h) divided by the instructed speed SC is the roadway surface condition (0= rainy/wet surface, 1=dry) The machine learning models are evaluated using relative and absolute prediction errors. The relative error is computed as the mean absolute percentage error (MAPE) using Equation (1). This error is the average absolute percentage change between the predicted and the true values. The corresponding absolute error is presented by the mean absolute error MAE using Equation (2). This error is the absolute difference between the predicted and the true values. J

�y𝑗𝑗 − y�𝚥𝚥 � 100 � MAPE = J y𝑗𝑗 J

Where

(1)

j=1

1 MAE = ��y𝑗𝑗 − y�𝚥𝚥 � J j=1

(2)

J = total number of observations in the testing data set, y = ground truth traffic state, and y� = predicted traffic state. For each machine learning algorithm, the average of MAE and MAPE are calculated using the 10-fold-cross-validation method. In the 10-fold-cross-validation method approach, the data set is divided into 10 chunks of data (folds). Then, the regression model is built using 9 folds and the unused fold. This driver is used to test the model. The entire process is repeated where each fold is used once as a test and the average MAE and MAPE are calculated across all folds. 4.1

Classification and Regression Tree

The Classification and Regression Tree (CART) model was implemented using Matlab. Pruning was applied to prune the tree at different levels. The MAE and MAPE obtained from a 10-fold Cross-Validation at different Pruning are used to find the best tree.

Fig 1. The CART model for the PRT.

Fig 2. The CART model for the deceleration level.

Fig 1 shows the regression trees that model the PRT and deceleration level. The CART that model the PRT has an average MAE equals 0.1212 seconds. As shown Fig 1all the predictors appear in the tree and the root of the tree is the grade. Fig 2 shows

the tree that model the deceleration level. This tree uses the TTI, Ge, and SC and find the other three predictors are not necessary to predict the deceleration level. The CART that model the deceleration level has an average MAE equals 0.3586 m/s2. 4.2

Random Forests

The Random Forest (RF) model was implemented using Matlab. In order to find the sufficient number of trees that gives the best result we did sensitivity analysis. We grow the forest from 5 to 50, using 50 trees step. After approximately 30 trees, no benefit is gained by including more trees. Thus, to apply RF to model the PRT and deceleration level, 50 trees were used, which is a sufficiently large number. The RF that model the deceleration level has an average MAE equals 0.1070 sec for the PRT and 0.3406 m/s2 for the deceleration level. 4.3

Ensemble of deep networks

The Ensemble of deep networks model was implemented using Matlab. In general, deep learning needs large data to avoid overfitting and give good performance. In order to overcome this problem we used an ensamble of deep network each on has two hidden layers and the number of neurons in the first and second hidden layers changed from 2 to 12 and from 5 to 20 respectively. The total number of deep networks in the ensemble is 167, which gives an average MAE equals 0.1070 sec for the PRT and 0.3406 m/s2 for the deceleration level. 4.4

Adaptive Boosting

The Adaptive Boosting (Adaboost model was implemented using Matlab. We did sensitivity analysis to find best number of weak learner. We found Adaboost using 50 trees is sufficient to model our dataset. The Adaboost has an average MAE equals 0.1141 sec for the PRT and 0.3314 m/s2 for the deceleration level. 4.5

Models Comparison

In this section, we show the tables which compare between the different machine learning algorithms we used to model the PRT and the deceleration level. For the sake of completeness, we include the MAE and MAPE when using the multiple linear regression (MLR). As shown in Table 1 the machine learning algorithms give better PRT prediction than MLR except CART. It is also shown that RF is the best algorithm. Table 2 shows the predictions error for the deceleration level and all machine learning algorithms has lower errors than the MLR. Table 2 shows that the ensemble of deep networks gives the best prediction.

Table 1: The mean of MAPE (%) and MAE (sec) for PRT Algorithm

Mean MAPE

Mean MAE

MLR CART Random forest Ensemble of deep networks Adaboost

16.1140 16.5435 14.5782 15.5386 14.6113

0.1180 0.1212 0.1070 0.1141 0.1074

Table 2: The mean of MAPE (%) and MAE (m/s2) for deceleration level

5

Algorithm

Mean MAPE

Mean MAE

MLR CART Random forest Ensemble of deep networks Adaboost

10.8734 10.2287 9.6866 9.3650 9.6074

0.3802 0.3586 0.3406 0.3314 0.3397

Conclusions

In this paper, we adopt several machine learning algorithms to model the brake PRT and the deceleration level. The built models could be used to predict PRT and the deceleration level at good accuracy. The adopted algorithms have the advantage of being non-parametric algorithms and they avoid many of the MLR assumptions such as normality and equal variance. The results obtained by modeling data set collected from two controlled experiments done at the smart road at VTTI show that machine learning algorithms are promising techniques in modeling PRT and deceleration level. We compared the adopted machine learning techniques and MLR using the prediction errors. For the PRT, all adopted machine learning techniques are better than the MLR except the CART, besides the RF gives the best prediction. For the deceleration level, MLR gave the worst predictions while the ensemble of deep networks gives the best prediction. In the near future when vehicle to infrastructure communication will be deployed, the signal controllers at intersections could use the developed machine learning models in conjunction with classification algorithms to detect the behavior of the driver if the signal is turned into yellow. Then it predicts the PRT and deceleration levels for the expected stopping drivers. Based on the prediction of these two quantities it could decide to extend the green to avoid any potential crashes at the intersection.

Acknowledgments The authors acknowledge the support of Ahmed Amer, Huan Li, and the other research assistants at the Center for Sustainable Mobility, VTTI for running the tests, and to the Center for Technology Development and the Smart Road Operations Group

at VTTI. This work was supported in part by grants from the Virginia Transportation Research Council (VTRC), the Mid-Atlantic Universities Transportation Center (MAUTC), and SAFETEA-LU funding.

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