^{1}

^{1}

^{1}

With the increase of hazardous materials (Hazmat) demand and transportation, frequent Hazmat road transportation accidents had arisen the widespread concern in the community. Thus, it is necessary to analyze the risk factors’ implications, which would make the safety of Hazmat transportation evolve from “passive type” to “active type”. In order to explore the influence of risk factors resulting in accidents and predict the occurrence of accidents under the combination of risk factors, 839 accidents that have occurred for the period 2015–2016 were collected and examined. The Bayesian network structure was established by experts’ knowledge using Dempster-Shafer evidence theory. Parameter learning was conducted by the Expectation-Maximization (EM) algorithm in Genie 2.0. The two main results could be likely to obtain the following. (1) The Bayesian network model can explore the most probable factor or combination leading to the accident, which calculated the posterior probability of each risk factor. For example, the importance of three or more vehicles in an accident leading to the severe accident is higher than less vehicles, and in the absence of other evidences, the most probable reasons for “explosion accident” are vehicles carrying flammable liquids, larger quantity Hazmat, vehicle failure, and transporting in autumn. (2) The model can predict the occurrence of accident by setting the influence degrees of specific factor. Such that the probability of rear-end accidents caused by “speeding” is 0.42, and the probability could reach up to 0.97 when the driver is speeding at the low-class roads. Moreover, the complex logical relationship in Hazmat road transportation accidents could be obtained, and the uncertain relation among various risk factors could be expressed. These findings could provide theoretical support for transportation corporations and government department on taking effective measures to reduce the risk of Hazmat road transportation.

In recent years, the demand for hazardous materials (Hazmat) has increased, resulting in increasing transportation requirement. More than 95% Hazmat require off-site transportation in China, and 63% are transported by road in Brazil, as well as 90% in the United States [

Hazmat transportation accidents would be able to produce catastrophic influence on human health, public safety, environment, and property due to the special characteristic of Hazmat, attracting more attention from general public and government on the management of Hazmat road transportation. Thus, how to improve the transportation condition and reduce the risk of transportation have become important and urgent problems for the industrial development. A growing amount studies about Hazmat transportation and production have been conducted [

The purpose of this study is to explore risk factors to reduce the risk of Hazmat road transportation. Many studies have been conducted by using statistical methods. Haastrup and Brockhoff [

Although statistical methods could analyze the relationships between accidents and the risk factors, they cannot account for the interplay among different factors and fail to reflect the fact that an accident is not usually the result of a single factor [

However, despite many studies on the traffic accidents and Hazmat accidents, most of them are studied based on the analysis of specific, isolated, and single factor [

The Hazmat transportation accident data was obtained from State Work Accident Briefing System, and Chemical Accidents Information Network for two years (2015-2016) in China, and the weather data was obtained from the China Meteorological Administration. The regional distribution of Hazmat transportation accidents is shown in Figure

Variables of Hazmat road transportation accidents.

Factors | Variables | Variables description | Discretization | Frequency | Percentage |
---|---|---|---|---|---|

Hazmat factors | Hazmat categories | Explosives | 1 | 27 | 3.20% |

Toxic gases | 2 | 158 | 18.90% | ||

Flammable liquids | 3 | 429 | 51.10% | ||

Corrosives | 4 | 121 | 14.40% | ||

others | 5 | 104 | 12.40% | ||

Quantity of Hazmat | <10 | 1 | 127 | 15.10% | |

10-24 | 2 | 284 | 33.80% | ||

25-39 | 3 | 358 | 42.70% | ||

≥40 | 4 | 70 | 8.40% | ||

Driver factors | Age | 24-35 | 1 | 144 | 17.20% |

36-45 | 2 | 644 | 76.70% | ||

46-60 | 3 | 51 | 6.10% | ||

Behaviors | Inappropriate driving | 1 | 13 | 1.50% | |

Speeding | 2 | 36 | 4.30% | ||

Fatigue driving | 3 | 20 | 2.40% | ||

Normal driving | 4 | 770 | 91.80% | ||

Location factors | Accident location | Group one | 1 | 360 | 42.90% |

Group two | 2 | 336 | 40.00% | ||

Group three | 3 | 59 | 7.00% | ||

Group four | 4 | 84 | 10.10% | ||

Special section | Intersection | 1 | 18 | 2.10% | |

Freeway service areas | 2 | 50 | 6.00% | ||

Toll stations | 3 | 78 | 9.30% | ||

Gas stations | 4 | 23 | 2.70% | ||

Normal | 5 | 670 | 79.90% | ||

Road surface | Dry | 1 | 794 | 94.60% | |

Wet | 2 | 45 | 5.40% | ||

Environment factors | Season | Spring | 1 | 227 | 27.10% |

Summer | 2 | 258 | 30.70% | ||

Autumn | 3 | 186 | 22.20% | ||

Winter | 4 | 168 | 20.00% | ||

Weekly distribution | Weekends | 1 | 198 | 23.60% | |

Weekdays | 2 | 641 | 76.40% | ||

Weather | Sunny | 1 | 202 | 24.10% | |

Cloudy | 2 | 347 | 41.40% | ||

Rainy & snow | 3 | 268 | 31.90% | ||

Fog & haze | 4 | 22 | 2.60% | ||

Visibility | dawn | 1 | 94 | 11.20% | |

day | 2 | 409 | 48.70% | ||

dusk | 3 | 60 | 7.20% | ||

dark | 4 | 276 | 32.90% | ||

Vehicle factors | Total vehicle involved in accident | 1 | 1 | 503 | 59.90% |

2 | 2 | 276 | 32.90% | ||

3 | 3 | 31 | 3.70% | ||

≥4 | 4 | 29 | 3.50% | ||

Type of vehicle | Bus & Truck | 1 | 13 | 1.55% | |

Private cars & Truck | 2 | 42 | 5.01% | ||

Non-motor & Truck | 3 | 11 | 1.31% | ||

Bus&Private cars&Truck | 4 | 10 | 1.19% | ||

Trucks | 5 | 763 | 90.94% | ||

Accidents factors | Accident type | Rear-end | 1 | 189 | 22.50% |

Sideswipe | 2 | 20 | 2.40% | ||

Rollover | 3 | 340 | 40.50% | ||

Collision | 4 | 145 | 17.30% | ||

Vehicle failure | 5 | 145 | 17.30% | ||

Accident consequence | Explosion | 1 | 25 | 3.00% | |

Fire | 2 | 96 | 11.40% | ||

Spill | 3 | 682 | 81.30% | ||

Non-spill | 4 | 36 | 4.30% | ||

Severity of accident | No injury | 1 | 656 | 78.19% | |

Severe injury | 2 | 139 | 16.57% | ||

Fatality | 3 | 44 | 5.24% |

Regional distribution of accidents.

Bayesian network is considered as the effective method to describe the causality between the risk factors and the output in the system, also referred to as the belief network. The Bayesian network is a Directed Acyclic Graph (DAG) and nodes represent variable status, while the directed edges represent dependencies between variables. The relationship or confidence coefficient between variables could be described by using Conditional Probability Table (CPT). The Bayesian formula is considered as the basis for the Bayesian network model, which could be expressed as

The construction of the Bayesian network model consists of following steps:

(1) Parameter determination: analyze the risk factors of Hazmat road transportation, and determine the variables needed for modeling (nodes of the Bayesian network), which could be shown in Table

(2) Structure learning: determine the dependencies or independencies relationships between variables (nodes), so that a directed acyclic network structure was constructed.

(3) Parameter learning: based on the given Bayesian network structure, determine the CPT for each node, and the dependence relationship between random variables could be described quantitatively.

The scientific network structure needs continuous iterations. At present, there are three methods to construct a Bayesian network structure [

The Bayesian network structure for Hazmat road transportation accidents.

(1) Establish a preliminary Bayesian network structure based on the assumptions of model.

(2) Use Delphi method to determine the relationship between risk factors. In general, there are four possible relationships between variables:

The relationship between variables cannot be determined, which could be represented as

There is no relationship between variables, which could be represented as

(3) Synthesize results from multiple experts. D-S evidence theory is used to reduce the subjectivity of experts’ knowledge, and the correlation between variables could be determined. The Dempster synthesis rule formula could be expressed as

(4) As the relationship of variables cannot be obtained by Delphi and D-S evidence theory, the mutual information value of variables should be calculated. And the entropy can be expressed as

Conditional entropy is a measure of the uncertainty of a random variable

Before obtaining

There are missing data on Hazmat road transportation accidents; the Expectation- Maximization (EM) algorithm is considered as the effective method to perform the maximum likelihood estimation for a set of parameters

Consider that

The guidance for the variable selection and classification were followed by the analysis of accident data and previous studies [

The Bayesian network model after parameter learning in Genie 2.0.

The Bayesian network could be used to calculate the posterior probability of risk factors under conditions of an accident and obtain the most likely factors or combinations that caused accidents. Set the “explosion” in “accident consequence” as the example to explore the causal inference, and the evidence variable is “explosion”. As shown in Figure

Posterior probability when the variable is “explosion”.

In addition, if the “fatality” in the “severity of accident” is considered as the evidence variable, the probability change of “total vehicle involved accident” could be obtained. The probability of “three” increases from 4% to 11%, and “more than three” is increasing from 3% to 9%. This may be explained by the fact that the importance of 3 or more vehicles in an accident leads to the severe accident being higher than less vehicles. Moreover, as for the accident consequence, the probability of “spill” decreases; meanwhile the “explosion” (3% to 6%) and fire (11% to 18%) have increased. Due to the special characteristic of Hazmat, explosion and fire would cause a larger area affected and can easily result in casualties, especially in the urban road and higher population densities [

Based on the bidirectional reasoning, not only could the Bayesian network model obtain the risk factors or the combination caused accidents, but also the probability of accidents could be calculated under the risk factors or combination, for example, in Genie, setting the “speeding” in “driver behavior” as an evidence variable, meaning that the status of evidence variable is considered as 100%. As can be seen from Figure

Accident prediction when the evidence variable is “speeding”.

As shown in Figure

Accident prediction when the evidence variable are “speeding” and “Group four”.

Flammable liquids have the highest posterior probability (0.51) and would easily result in explosion. This could be explained by that increasing demand for the flammable liquid and decreasing reliability of transporting flammable liquids due to the single-mode packaging. The quantity of Hazmat transported would significantly affect the severity of accident. The larger the quantity of Hazmat transportation, the larger the inertia of the transportation vehicles, making it not easy to control the emergency [

Previous studies have shown the relationship between driver’s age and the severity of accidents [

The model results show that “Group one” (the posterior probability is 0.43) and “Group two” (the posterior probability is 0.40) in “accident location” are likely to be associated with severe accidents, which could be attributed by the combination of higher average speed and larger speed dispersion. More importantly, “Group one” and “Group two” roads are considered as the major transport corridors for Hazmat [

Hazmat road transportation accidents would easily occur at summer (the posterior probability is 0.31), which is attributed to the characteristic of Hazmat, such as flammable and explosive. And the posterior probability of accidents occurring at weekdays is 0.76, which could be explained by that freeway could be toll-free on important holidays, resulting in significant increase of traffic volume, which could decrease the speed of vehicles. Moreover, Hazmat transportation vehicles were not allowed to drive on freeway (Pan, 2013). Weather is a significant factor for the Hazmat transportation, with cloudy having the highest posterior probability (0.41) followed by rainy (0.32). This could be ascribed that the driver’s mood and visual would be decreased in cloudy and rainy, and the rainy would lower the friction coefficient of roads due to the thin film of water existing between the road surface and tires, which could make the road slippery, increasing the braking distance effectively [

As for the total vehicles involved in accident, “more than three” would easily result in higher severity of accidents. And the private car involved in accident would cause the severe accident. Two reasons could explain these findings: one is that more vehicles would cause more people involved in accidents, resulting in more people injured; another one is the disparity in mass and speed of trucks compared to other vehicles. In case of an accident, lighter vehicles (such as private cars) usually absorb the greatest part of the kinetic energy and suffer from more severe injury.

Many studies have shown the significant relationship of accidents type and severity, indicating that the rollover accident is associated with the higher severity of accident [

In summary, the occurrence of Hazmat road transportation accidents is unexpected, random, dangerous, and potential. Frequent accidents imply that it is necessary to explore risk factors by using accident mechanism. Bayesian network is the effective method to deal with uncertainties, which exhibit the potential hierarchical relation by the Directed Acyclic Graph. In the paper, the Bayesian network was developed based on experts’ knowledge and modified based on the Hazmat road transportation accident data (N=839) in China. The Bayesian network structure was established by using Genie 2.0, and the results of network structure model reveal the influence of risk factors resulting in accidents and the relationship among risk factors. The study shows that the posterior probability of the Bayesian network could provide effective method for finding the important factors and the factors combination of accidents. These findings could provide theoretical guidance, which could help transportation corporations and government departments take necessary measures to reduce the frequency of Hazmat accidents. More importantly, it must be noted that the aforementioned results were obtained by analyzing the data sample collected from State Work Accident Briefing System and Hazardous Chemical Accidents Communications, which could be existing limitations. As for the further studies, the conclusions should be more generalizable if the dataset had larger size of sample and accidents from multiple states.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This study has been supported by projects of the National Natural Science Foundation of China (no. 71671127).