Multimodal injury risk analysis of road users at signalized and non-signalized intersections

This paper proposes a multimodal approach to study safety at intersections by simultaneously analysing the safety and flow outcomes for both motorized and non-motorized traffic. This study uses an extensive inventory of signalized and non-signalized intersections on the island of Montreal, Quebec, Canada, containing disaggregate motor-vehicle, cyclist and pedestrian flows, injury data, geometric design, traffic control and built environment characteristics in the vicinity of each intersection. Bayesian multivariate Poisson models are used to analyze the injury and traffic flow outcomes and to develop safety performance functions for each mode at both facilities. After model calibration, contributing injury frequency factors are identified. Injury frequency and injury risk measures are then generated to carry out a comparative study to identify which mode is at greatest risk at intersections in Montreal. Among other results, this study identified the significant effect that motor-vehicle traffic imposes on cyclist and pedestrian injury occurrence. Motor-vehicle traffic is the main risk determinant for all injury and intersection types. This highlights the need for safety improvements for cyclists and pedestrians who are, on average, at 14 and12 times greater risk than motorists, respectively, at signalized intersections. Aside from exposure measures, this work also identifies some geometric design and built environment characteristics affecting injury occurrence for cyclists, pedestrians and motor-vehicle occupants.     

Estimating the risk of collisions between bicycles and motor vehicles at signalized intersections

Collisions between bicycles and motor vehicles have caused severe life and property losses in many countries. The majority of bicycle-motor vehicle (BMV) accidents occur at intersections. In order to reduce the number of BMV accidents at intersections, a substantial understanding of the causal factors for the collisions is required. In this study, intersection BMV accidents were classified into three types based on the movements of the involved motor vehicles and bicycles. The three BMV accident classifications were through motor vehicle related collisions, left-turn motor vehicle related collisions, and right-turn motor vehicle related collisions. A methodology for estimating these BMV accident risks was developed based on probability theory. A significant difference between this proposed methodology and most current approaches is that the proposed approach explicitly relates the risk of each specific BMV accident type to its related flows. The methodology was demonstrated using a 4-year (1992-1995) data set collected from 115 signalized intersections in the Tokyo Metropolitan area. This data set contains BMV accident data, bicycle flow data, motor vehicle flow data, traffic control data, and geometric data for each intersection approach. For each BMV risk model, an independent explanatory variable set was chosen according to the characteristics of the accident type. Three negative binomial regression models (one corresponding to each BMV accident type) were estimated using the maximum likelihood method. The coefficient value and its significance level were estimated for each selected variable. The negative binomial dispersion parameters for all the three models were significant at 0.01 levels. This supported the choice of the negative binomial regression over the Poisson regression for the quantitative analyses in this study.     

Applying Bayesian hierarchical models to examine motorcycle crashes at signalized intersections

Motorcycles are overrepresented in road traffic crashes and particularly vulnerable at signalized intersections. The objective of this study is to identify causal factors affecting the motorcycle crashes at both four-legged and T signalized intersections. Treating the data in time-series cross-section panels, this study explores different Hierarchical Poisson models and found that the model allowing autoregressive lag-1 dependence specification in the error term is the most suitable. Results show that the number of lanes at the four-legged signalized intersections significantly increases motorcycle crashes largely because of the higher exposure resulting from higher motorcycle accumulation at the stop line. Furthermore, the presence of a wide median and an uncontrolled left-turn lane at major roadways of four-legged intersections exacerbate this potential hazard. For T signalized intersections, the presence of exclusive right-turn lane at both major and minor roadways and an uncontrolled left-turn lane at major roadways increases motorcycle crashes. Motorcycle crashes increase on high-speed roadways because they are more vulnerable and less likely to react in time during conflicts. The presence of red light cameras reduces motorcycle crashes significantly for both four-legged and T intersections. With the red light camera, motorcycles are less exposed to conflicts because it is observed that they are more disciplined in queuing at the stop line and less likely to jump start at the start of green.     

The link between built environment, pedestrian activity and pedestrian-vehicle collision occurrence at signalized intersections

This paper studies the influence of built environment (BE) – including land use types, road network connectivity, transit supply and demographic characteristics – on pedestrian activity and pedestrian–vehicle collision occurrence. For this purpose, a two-equation modeling framework is proposed to investigate the effect of built environment on both pedestrian activity and vehicle–pedestrian collision frequency at signalized intersections. Using accident data of ambulance services in the City of Montreal, the applicability of our framework is illustrated. Different model settings were attempted as part of a model sensitivity analysis. Among other results, it was found that the BE in the proximity of an intersection has a powerful association with pedestrian activity but a small direct effect on pedestrian–vehicle collision frequency. This suggests that the impact of BE is mainly mediated through pedestrian activity. In other words, strategies that encourage densification, mix of land uses and increase in transit supply will increase pedestrian activity and may indirectly, with no supplementary safety strategies, increase the total number of injured pedestrians. In accordance with previous research, the number of motor vehicles entering a particular intersection is the main determinant of collision frequency. Our results show that a 30% reduction in the traffic volume would reduce the total number of injured pedestrians by 35% and the average risk of pedestrian collision by 50% at the intersections under analysis. Major arterials are found to have a double negative effect on pedestrian safety. They are positively linked to traffic but negatively associated with pedestrian activity. The proposed framework is useful for the identification of effective pedestrian safety actions, the prediction of pedestrian volumes and the appropriate safety design of new urban developments that encourage walking.     

Gender differences in injury severity risks in crashes at signalized intersections

This paper analyzes gender differences in crash risk severities using data for signalized intersections. It estimates gender models for injury severity risks and finds that driver condition, type of crash, type of vehicle driven and vehicle safety features have different effects on females’ and males’ injury severity risks. Also, it finds some variables which are significantly related to females’ injury severity risks but not males’ and others which affect males’ injury severity risks but not females’. It concludes that better and more in-depth information about gender differences in injury severity risks is gained by estimating separate models for females and males.     

Exploring the overall and specific crash severity levels at signalized intersections

Many studies have shown that intersections are among the most dangerous locations of a roadway network. Therefore, there is a need to understand the factors that contribute to injuries at such locations. This paper addresses the different factors that affect crash injury severity at signalized intersections. It also looks into the quality and completeness of the crash data and the effect that incomplete data has on the final results. Data from multiple sources have been cross-checked to ensure the completeness of all crashes including minor crashes that are usually unreported or not coded into crash databases. The ordered probit modeling technique has been adopted in this study to account for the fact that injury levels are naturally ordered variables. The tree-based regression methodology has also been adopted in this study to explore the factors that affect each severity level. The probit model results showed that a combination of crash-specific information and intersection characteristics result in the highest prediction rate of injury level. More specifically, having a divided minor roadway or a higher speed limit on the minor roadway decreased the level of injury while crashes involving a pedestrian/bicyclist and left turn crashes had the highest probability of a more severe crash. Several regression tree models showed a difference in the significant factors that affect the different severity types. Completing the data with minor non injury crashes improved the modeling results and depicted differences when modeling the no injury crashes.     

Temporal and spatial analyses of rear-end crashes at signalized intersections

In this study, the generalized estimating equations with the negative binomial link function were used to model rear-end crash frequencies at signalized intersections to account for the temporal or spatial correlation among the data. The longitudinal data for 208 signalized intersections over 3 years and the spatially correlated data for 476 signalized intersections which are located along different corridors were collected in the state of Florida. The modeling results showed that there are high correlations between the longitudinal or spatially correlated rear-end crashes. Some intersection related variables are identified as significantly influencing rear-end crash occurrences at signalized intersections. Intersections with heavy traffic on the major and minor roadways, having more right and left-turn lanes on the major roadway, having a large number of phases per cycle (indicated by the left-turn protection on the minor roadway), with high speed limits on the major roadway, and in high population areas are correlated with high rear-end crash frequencies. On the other hand, intersections with three legs, having channelized or exclusive right-turn lanes on the minor roadway, with protected left-turning on the major roadway, with medians on the minor roadway, and having longer signal spacing have a lower frequency of rear-end crashes.     

Severity of driver injury and vehicle damage in traffic crashes at intersections: a Bayesian hierarchical analysis

Most crash severity studies ignored severity correlations between driver-vehicle units involved in the same crashes. Models without accounting for these within-crash correlations will result in biased estimates in the factor effects. This study developed a Bayesian hierarchical binomial logistic model to identify the significant factors affecting the severity level of driver injury and vehicle damage in traffic crashes at signalized intersections. Crash data in Singapore were employed to calibrate the model. Model fitness assessment and comparison using intra-class correlation coefficient (ICC) and deviance information criterion (DIC) ensured the suitability of introducing the crash-level random effects. Crashes occurring in peak time and in good street-lighting condition as well as those involving pedestrian injuries tend to be less severe. But crashes that occur in night time, at T/Y type intersections, and on right-most lane, as well as those that occur in intersections where red light cameras are installed tend to be more severe. Moreover, heavy vehicles have a better resistance on severe crash and thus induce less severe injuries, while crashes involving two-wheel vehicles, young or aged drivers, and the involvement of offending party are more likely to result in severe injuries.     

Differences in passenger car and large truck involved crash frequencies at urban signalized intersections: An exploratory analysis

The influence of intersection features on safety has been examined extensively because intersections experience a relatively large proportion of motor vehicle conflicts and crashes. Although there are distinct differences between passenger cars and large trucks-size, operating characteristics, dimensions, and weight-modeling crash counts across vehicle types is rarely addressed. This paper develops and presents a multivariate regression model of crash frequencies by collision vehicle type using crash data for urban signalized intersections in Tennessee. In addition, the performance of univariate Poisson-lognormal (UVPLN), multivariate Poisson (MVP), and multivariate Poisson-lognormal (MVPLN) regression models in establishing the relationship between crashes, traffic factors, and geometric design of roadway intersections is investigated. Bayesian methods are used to estimate the unknown parameters of these models. The evaluation results suggest that the MVPLN model possesses most of the desirable statistical properties in developing the relationships. Compared to the UVPLN and MVP models, the MVPLN model better identifies significant factors and predicts crash frequencies. The findings suggest that traffic volume, truck percentage, lighting condition, and intersection angle significantly affect intersection safety. Important differences in car, car–truck, and truck crash frequencies with respect to various risk factors were found to exist between models. The paper provides some new or more comprehensive observations that have not been covered in previous studies.     

Calibration and validation of simulated vehicle safety performance at signalized intersections

A systematic procedure is presented for calibrating and validating a microscopic model of safety performance. The context in the model application is the potential for rear-end crashes at signalized intersections. VISSIM^® v.4.3 provides the simulation platform for estimating the safety performance for individual vehicles and has been calibrated and validated using separate samples of observed vehicle tracking data extracted from the FHWA/NGSIM program. The calibration exercise involves four sequential steps: (1) heuristic selection of initial model inputs, (2) statistical screening using a Plackett–Burnman design, (3) fractional factorial analysis relating inputs to safety performance, and (4) genetic algorithm procedure for obtaining best estimate input values. Three measures of safety performance were considered: crash potential index, number of vehicles in conflict and total conflict duration per vehicle. Model consistency was assessed by comparing simulated and observed safety performance based on a separate validation sample of vehicle tracking data. The suggested procedure was found to effectively estimate model input parameters that closely matched safety performance measures in the observed validation data. This procedure yields an objective and efficient means for simulation model calibration applied for estimating safety performance at signalized intersections.     

An accelerated failure time model for investigating pedestrian crossing behavior and waiting times at signalized intersections

The waiting process is crucial to pedestrians in the street-crossing behavior. Once pedestrians terminate their waiting behavior during the red light period, they would cross against the red light and put themselves in danger. A joint hazard-based duration model is developed to investigate the effect of various covariates on pedestrian crossing behavior and to estimate pedestrian waiting times at signalized intersections. A total of 1181 pedestrians approaching the intersections during red light periods were observed in Beijing, China. Pedestrian crossing behaviors are classified into immediate crossing behavior and waiting behavior. The probability and effect of various covariates for pedestrians’ immediate crossing behavior are identified by a logit model. Four accelerated failure time duration models based on the exponential, Weibull, lognormal and log-logistic distributions are proposed to examine the significant risk factors affecting duration times for pedestrians’ waiting behavior. A joint duration model is developed to estimate pedestrian waiting times. Moreover, unobserved heterogeneity is considered in the proposed model. The results indicate that the Weibull AFT model with shared frailty is appropriate for modelling pedestrian waiting durations. Failure to account for heterogeneity would significantly underestimate the effects of covariates on waiting duration times. The proposed model provides a better understanding of pedestrian crossing behavior and more accurate estimation of pedestrian waiting times. It may be applicable in traffic system analysis in developing countries with high flow of mixed traffic.     

Safety surrogate histograms (SSH): A novel real-time safety assessment of dilemma zone related conflicts at signalized intersections

Drivers’ indecisiveness in dilemma zones (DZ) could result in crash-prone situations at signalized intersections. DZ is to the area ahead of an intersection in which drivers encounter a dilemma regarding whether to stop or proceed through the intersection when the signal turns yellow. An improper decision to stop by the leading driver, combined with the following driver deciding to go, can result in a rear-end collision, unless the following driver recognizes a collision is imminent and adjusts his or her behavior at or shortly after the onset of yellow. Considering the significance of DZ-related crashes, a comprehensive safety measure is needed to characterize the level of safety at signalized intersections. In this study, a novel safety surrogate measure was developed utilizing real-time radar field data. This new measure, called safety surrogate histogram (SSH), captures the degree and frequency of DZ-related conflicts at each intersection approach. SSH includes detailed information regarding the possibility of crashes, because it is calculated based on the vehicles conflicts. An example illustrating the application of the new methodology at two study sites in Virginia is presented and discussed, and a comparison is provided between SSH and other DZ-related safety surrogate measures mentioned in the literature. The results of the study reveal the efficacy of the SSH as complementary to existing surrogate measures.     

Multivariate random-parameters zero-inflated negative binomial regression model: An application to estimate crash frequencies at intersections

Crash data are collected through police reports and integrated with road inventory data for further analysis. Integrated police reports and inventory data yield correlated multivariate data for roadway entities (e.g., segments or intersections). Analysis of such data reveals important relationships that can help focus on high-risk situations and coming up with safety countermeasures. To understand relationships between crash frequencies and associated variables, while taking full advantage of the available data, multivariate random-parameters models are appropriate since they can simultaneously consider the correlation among the specific crash types and account for unobserved heterogeneity. However, a key issue that arises with correlated multivariate data is the number of crash-free samples increases, as crash counts have many categories. In this paper, we describe a multivariate random-parameters zero-inflated negative binomial (MRZINB) regression model for jointly modeling crash counts. The full Bayesian method is employed to estimate the model parameters. Crash frequencies at urban signalized intersections in Tennessee are analyzed. The paper investigates the performance of MZINB and MRZINB regression models in establishing the relationship between crash frequencies, pavement conditions, traffic factors, and geometric design features of roadway intersections. Compared to the MZINB model, the MRZINB model identifies additional statistically significant factors and provides better goodness of fit in developing the relationships. The empirical results show that MRZINB model possesses most of the desirable statistical properties in terms of its ability to accommodate unobserved heterogeneity and excess zero counts in correlated data. Notably, in the random-parameters MZINB model, the estimated parameters vary significantly across intersections for different crash types.     

Illegal pedestrian crossing at signalised intersections: Incidence and relative risk

Illegal pedestrian behaviour is common and is reported as a factor in many pedestrian crashes. Since walking is being promoted for its health and environmental benefits, minimisation of its associated risks is of interest. The risk associated with illegal road crossing is unclear, and better information would assist in setting a rationale for enforcement and priorities for public education. An observation survey of pedestrian behaviour was conducted at signalised intersections in the Brisbane CBD (Queensland, Australia) on typical workdays, using behavioural categories that were identifiable in police crash reports. The survey confirmed high levels of crossing against the lights, or close enough to the lights that they should legally have been used. Measures of exposure for crossing legally, against the lights, and close to the lights were generated by weighting the observation data. Relative risk ratios were calculated for these categories using crash data from the observation sites and adjacent midblocks. Crossing against the lights and crossing close to the lights both exhibited a crash risk per crossing event approximately eight times that of legal crossing at signalised intersections. The implications of these results for enforcement and education are discussed, along with the limitations of the study.     

A Bayesian Belief Network modelling of organisational factors in risk analysis: A case study in maritime transportation

The paper presents an innovative approach to integrate Human and Organisational Factors (HOF) into risk analysis. The approach has been developed and applied to a case study in the maritime industry, but it can also be utilised in other sectors. A Bayesian Belief Network (BBN) has been developed to model the Maritime Transport System (MTS), by taking into account its different actors (i.e., ship-owner, shipyard, port and regulator) and their mutual influences. The latter have been modelled by means of a set of dependent variables whose combinations express the relevant functions performed by each actor. The BBN model of the MTS has been used in a case study for the quantification of HOF in the risk analysis carried out at the preliminary design stage of High Speed Craft (HSC). The study has focused on a collision in open sea hazard carried out by means of an original method of integration of a Fault Tree Analysis (FTA) of technical elements with a BBN model of the influences of organisational functions and regulations, as suggested by the International Maritime Organisation's (IMO) Guidelines for Formal Safety Assessment (FSA). The approach has allowed the identification of probabilistic correlations between the basic events of a collision accident and the BBN model of the operational and organisational conditions. The linkage can be exploited in different ways, especially to support identification and evaluation of risk control options also at the organisational level. Conditional probabilities for the BBN have been estimated by means of experts’ judgments, collected from an international panel of different European countries. Finally, a sensitivity analysis has been carried out over the model to identify configurations of the MTS leading to a significant reduction of accident probability during the operation of the HSC.     

Comparative analysis of driver’s brake perception-reaction time at signalized intersections with and without countdown timer using parametric duration models

Countdown timers display the time left on the current signal, which makes drivers be more ready to react to the phase change. However, previous related studies have rarely explored the effects of countdown timer on driver’s brake perception-reaction time (BPRT) to yellow light. The goal of this study was therefore to characterize and model driver’s BPRT to yellow signal at signalized intersections with and without countdown timer. BPRT data for “first-to-stop” vehicles after yellow onset within the transitional zone were collected through on-site observation at six signalized intersections in Harbin, China. Statistical analysis showed that the observed 15th, 50th, and 85th percentile BPRTs without countdown timer were 0.52, 0.84, and 1.26 s, respectively. The observed 15th, 50th, and 85th percentile BPRTs with countdown timer were 0.32, 1.20, and 2.52 s, respectively. Log-logistic distribution appeared to best fit the BPRT without countdown timer, while Weibull distribution seemed to best fit the BPRT with countdown timer. After that, a Log-logistic accelerated failure time (AFT) duration model was developed to model driver’s BPRT without countdown timer, whereas a Weibull AFT duration model was established to model driver’s BPRT with countdown timer. Three significant factors affecting the BPRT identified in both AFT models included yellow-onset distance from the stop line, yellow-onset approach speed, and deceleration rate. No matter whether the presence of countdown timer or not, BPRT increased as yellow-onset distance to the stop line or deceleration rate increased, but decreased as yellow-onset speed increased. The impairment of driver’s BPRT due to countdown timer appeared to increase with yellow-onset distance to the stop line or deceleration rate, but decrease with yellow-onset speed. An increase in driver’s BPRT because of countdown timer may induce risky driving behaviors (i.e., stop abruptly, or even violate traffic signal), revealing a weakness of countdown timer in traffic safety aspect.     

Crash risk analysis for Shanghai urban expressways: A Bayesian semi-parametric modeling approach

Urban expressway systems have been developed rapidly in recent years in China; it has become one key part of the city roadway networks as carrying large traffic volume and providing high traveling speed. Along with the increase of traffic volume, traffic safety has become a major issue for Chinese urban expressways due to the frequent crash occurrence and the non-recurrent congestions caused by them. For the purpose of unveiling crash occurrence mechanisms and further developing Active Traffic Management (ATM) control strategies to improve traffic safety, this study developed disaggregate crash risk analysis models with loop detector traffic data and historical crash data. Bayesian random effects logistic regression models were utilized as it can account for the unobserved heterogeneity among crashes. However, previous crash risk analysis studies formulated random effects distributions in a parametric approach, which assigned them to follow normal distributions. Due to the limited information known about random effects distributions, subjective parametric setting may be incorrect. In order to construct more flexible and robust random effects to capture the unobserved heterogeneity, Bayesian semi-parametric inference technique was introduced to crash risk analysis in this study. Models with both inference techniques were developed for total crashes; semi-parametric models were proved to provide substantial better model goodness-of-fit, while the two models shared consistent coefficient estimations. Later on, Bayesian semi-parametric random effects logistic regression models were developed for weekday peak hour crashes, weekday non-peak hour crashes, and weekend non-peak hour crashes to investigate different crash occurrence scenarios. Significant factors that affect crash risk have been revealed and crash mechanisms have been concluded.     

Model calibration: A hierarchical Bayesian approach

Many geotechnical engineering models are empirical and calibrated based on data gathered from various sites/projects, using optimisation algorithms with criteria like least squared errors or minimising the coefficient of variation of method bias with the constraint of mean bias equal to unity. This paper discusses the use of hierarchical Bayesian regression models for the same purpose. A database of axial capacity of piles in predominantly clay sites and a CPT-based design model, compiled and developed as part of a Joint Industry Project (JIP) led by the Norwegian Geotechnical Institute (NGI), is used for demonstration. The analyses focus on two related areas that the traditional approaches overlook: (i) quantification of uncertainty in the estimated parameters of the model, and (ii) modelling site-dependency of the model parameters (i.e., between-group variation). The former is important in the context of reliability-based design and contributes to establishing confidence in estimated reliability indices, particularly when only limited data are available. The latter expands our understanding regarding the domain of applicability of a model; that is, if a model is broadly applicable or highly site-dependent. The benefits of the proposed Bayesian approach are highlighted with a prediction exercise where the calibrated models are used in conjunction with limited site or project-specific data.     

Nonlinear random vibration analysis: A Bayesian nonparametric approach

Random vibration analysis aims to estimate the response statistics of dynamical systems subject to stochastic excitations. Stochastic differential equations (SDEs) that govern the response of general nonlinear systems are often complicated, and their analytical solutions are scarce. Thus, a range of approximate methods and simulation techniques have been developed. This paper develops a hybrid approach that approximates the governing SDE of nonlinear systems using a small number of response simulations and information available a priori. The main idea is to identify a set of surrogate linear systems such that their response probability distributions collectively estimate the response probability distribution of the original nonlinear system. To identify the surrogate linear systems, the proposed method integrates the simulated responses of the original nonlinear system with information available a priori about the number and parameters of the surrogate linear systems. There will be epistemic uncertainty in the number and parameters of the surrogate linear systems because of the limited data. This paper proposes a Bayesian nonparametric approach, called a Dirichlet Process Mixture Model, to capture these uncertainties. The Dirichlet process models the uncertainty over an infinite-dimensional parameter space, representing an infinite number of potential surrogate linear systems. Specifically, the proposed method allows the number of surrogate linear systems to grow indefinitely as the nonlinear system observed dynamic unveil new patterns. The quantified uncertainty in the estimates of the unknown model parameters propagates into the response probability distribution. The paper then shows that, under some mild conditions, the estimated probability distribution approaches, as close as desired, to the original nonlinear system’s response probability distribution. As a measure of model accuracy, the paper provides the convergence rate of the response probability distribution. Because the posterior distribution of the unknown model parameters is often not analytically tractable, a Gibbs sampling algorithm is presented to draw samples from the posterior distribution. Variational Bayesian inference is also introduced to derive an approximate closed-form expression for the posterior distribution. The paper illustrates the proposed method through the random vibration analysis of a nonlinear elastic and a nonlinear hysteretic system.