3.2. Grid Division
The proposed grid management of the train operation department is a logical virtual grid with personnel participation; it has three-dimensional attributes: time, space, and event. The risk events of employees in any unit grid at any time can be accurately displayed in the “grids–elements–time” three-dimensional coordinate system, and it can organize the disordered and uncorrelated risk data so that railway managers can have a more comprehensive perception and grasp of when, where, and what risk may occur to employees in a short time and a small space, providing modeling support for personalized risk assessment.
Figure 2 shows the three-dimensional spatial relationship among grids, elements, and events. The work activities of employees can be reflected in the coordinate system of three-dimensional space, and the factor
is the
th element in the grid
, corresponding to events that occur at different moments:
,
, and
.
- (1)
Grid definition and coding
Cell grid definition and division method [
13]. The railway traffic work is organized and implemented in the station, and the working scope of the staff is centered on the mileage coordinates of the station center and bounded by the mileage coordinates of the signal machines in and out of the station. Therefore, the grid of the train operation department refers to the discretization of the plane space of various types of work areas covered by the mileage range of the station access signal, that is, it is divided into a number of discrete and unequal “small areas”. The “small areas” can be regarded as a collection of the working activities of several employees in any post, and each “small area” is denoted as a grid cell
,
, where
is the total number of train operation department grid units.
Based on the angle of job scope and spatial position, the grid division of the train operation department should represent the operation scope of all types of employees based on the area of two-dimensional space to realize the correlation between job operation and spatial position. For example,
Figure 3 shows the grid division diagram of ×× station in Shenshuo Railway, both the station attendant and the towerman work in the operation room, but they still belong to two different grids owing to different job boundaries.
Grid coding rule. Grid coding is related to geospatial dimension information, and grid data should include spatial and attribute data [
14]. Each cell grid should have a unique identifier. The transportation system grid coding should include “line code + position code + sequence code”, where the line code is 4 bits and the location code is expressed as the mileage of the station center in kilometers and is set to 4 digits according to the length of the line. The sequence code represents the sequence number of a grid in the station, which can be set as 2 digits. The sequence number starts from the direction of small mileage to the direction of large mileage in the station; thus, the grid code is set to 10 digits, as shown in
Figure 4.
- (2)
Definition and coding of grid elements
Individual employees and equipment of the train operation department grid are collectively referred to as grid elements. This study focuses on the study of an “individual employee” as a special element, which owns initiative and can carry out various production activities in the grid; thus, we establish the correlation between the grid and its elements. The train operation department generally implements “five shifts and four operations” (the working cycle is 20 days, 12 days on duty and 8 days off duty). Therefore, for the same post, there is a one-to-many relationship between the grid and “workers”. Therefore, a grid may contain one or more elements, but the elements can not cover multiple grids. Element encoding generally includes employee dimension information and geographic spatial dimension information. The employee dimension coding information is used to determine the work type of the employee, and the geographic spatial dimension coding information is used to determine the location of the employee, which can be expressed by the corresponding grid coding. The combination of these elements can help achieve the unique identification of the employee; therefore, the code is designed as “grid code + post type code + sequence code”. The post type code of an employee is set to 4 bits, and the sequence code represents the serial number of an employee in a certain grid, which is 2 bits; therefore, the overall code of grid elements is 16 bits (
Figure 5).
- (3)
Definition and encoding of grid events
The safety behavior information generated by elements in a cell grid at a certain moment is called the event of grid elements. Events of grid elements comprise events with positive or negative impacts, and events with negative impacts are known as risk events (this study focuses on risk events). The coded event should comprise two parts: event dimension information and element dimension information. The event dimension information can determine the category of the event, and the element dimension information should adopt the coding of the corresponding element of the event. Combined with the coding principle, the coding design is “element code + event category code + event code”. The event category code can be set as 2 bits, the event code can be set as 2 bits, and the total event code is 20 bits (
Figure 6).
3.4. Risk Analysis
- (1)
Risk assessment criteria
Probability level. Based on the relevant standards of the European Railway Industry [
30] and the opinions of railway field experts, the risk probability level is divided into five levels (
Table 3).
Severity level. Based on the relevant standards of the European Railway Industry [
30] and the opinions of railway field experts, the risk consequence severity level is divided into five levels (
Table 4).
Vulnerability level. At present, there is no unified classification standard for railway safety risk vulnerability at home or abroad. In this study, with reference to the research on vulnerability-related literature [
20] and the requirements of railway site safety management, vulnerability is divided into five levels (
Table 5).
Risk acceptance criteria. At present, the commonly used risk acceptance criteria include ALARP criteria in the UK, GAMAB criteria in France, and MEM criteria in Germany [
30,
31]. Among them, ALARP criteria have been widely used in railway, energy, finance, engineering construction, and other industries. In this study, the following standards are formulated with reference to ALARP standards (
Table 6). In this study, the “additive” relationship is used to represent the “combination” relationship between probability, severity, and vulnerability. The minimum value is 3 and the maximum value is 15. The summation value is divided into four levels according to expert suggestions.
- (2)
Weights of the hazard factors
In the transportation system, hazard factors of risk events belong to different grids, there is interaction and feedback between these hazard factors, and they have strong internal and external dependence. Many experts use the ANP method to study this dependence [
32,
33,
34,
35]. In this study, the ANP method is used to solve the relative weight of hazard factors as the input of the probability of safety behavior risk events. The specific steps are as follows:
Step 1: Construct the ANP hierarchy. The network structure of ANP consists of two parts: the control layer and the network layer, as shown in
Figure 7. In the control layer, there are control criteria
,
, …
, which are the criteria of relative objectives, such as risk, benefit, opportunity, and cost. These criteria are independent of each other and are only governed by the target element. The network layer is composed of a hazard subset
that is controlled by the control layer, and its internal structure is the network structure that influences each other. This study considers the single safety behavior risk of the transportation system, and this criterion is the target of risk analysis. Therefore, the ANP hierarchy includes the network layer, which comprises hazard factors governed by a single risk criterion and can be divided into multiple categories, whose internal structure is the network structure that affects each other.
Step 2: Calculate the unweighted hypermatrix. Assume that the network layer of the ANP includes a hazard subset
,
, …
, among which there are hazard factors
,
, ….,
,
. Under the single risk criterion, considering the hazard factor
in
as the secondary criterion, the elements in the hazard factor subset
are compared according to their influence on
; i.e., a judgment matrix is constructed under the single risk criterion, and the matrix
is obtained, as expressed in Equation (1).
Step 3: Establish the weighted super matrix
. Taking the entire hazard subset as an element, the relative importance of a certain hazard subset is pally compared under a single risk criterion, and the normalized weight vector
of the hazard subset under the subcriterion is obtained, where
represents the influence weight of the
th hazard subset on the
th hazard subset, “0” implies no influence, and
; then, the weighted super matrix is expressed by Equation (2).
Step 4: Calculate the limit hypermatrix . Calculate the limit relative ordering vector for each hypermatrix. If the limit converges and is unique, the value of the corresponding row of the original matrix is the weight of each index. The weight value of each index can be obtained by this formula.
- (3)
Probability calculation
The induced intensity of hazard factors refers to the probability of grid element risk events induced by hazards in a specific space-time state. The hazard induced intensity assignment function can establish a personalized function according to the uniqueness of the inducing factors of the risk events that occur in each grid element in a certain period of time and a specific operation area, solve the induced intensity of the hazard factor, and take it as the input for the calculation of the possibility of risk events. Due to the uncertainty of the safety behavior risk of the transportation system, the hazard factors in the cell grid will present different characteristics in different spatio-temporal states. When solving the induced intensity of the hazard factors, it is necessary to select the appropriate assignment function according to the actual situation of the cell grid. Common assignment functions include triangle function, trapezoidal function, Gaussian function, etc. This study presents an assignment function model for the induced intensity of disaster factors of element risk events in a cell grid. The model can select and assign an appropriate membership function according to the specific conditions of the hazard factors of element risk events in the cell grid to calculate the induced intensity of the hazard factors of element risk events in the grid more accurately. The model expression is expressed in Equation (3).
where
—In the time interval , the induced intensity of the hazard factor of a certain risk event in the cell grid is assigned.
—Mapping between variables and . The construction should conform to the actual situation of the transportation system, objectively reflect the intensity of the hazard factor , and be easy to calculate, avoiding manual intervention.
—Within the time interval , a certain state index related to the hazard factors of the grid element, such as professional level, educational level, weather temperature, etc.
—Represents the number of status indicators.
Through the personalized assignment of the induced intensity of hazard factors, combined with the weight of hazard factors obtained by the ANP method, this study creatively puts forward a possibility assignment function of safety behavior risk events, and the function formula is expressed in Equation (4).
where
is the weight coefficient, which satisfies Equation (5).
- (4)
Vulnerability calculation
Vulnerability is the inherent characteristic of employees’ safety behavior during risk events in the grid, which is externally reflected in their susceptibility to interference and vulnerability in risk events. The root of these characteristics lies in the coupling influence of various hazard factors in the grid. Therefore, the greater the coupling strength is, the stronger the vulnerability, and vice versa. The DEMATEL method is an effective method to analyze complex system problems. This method can overcome the disadvantage of the traditional risk assessment method, which assumes that the relationship between variables is independent of each other and can fully consider the interdependence of each element and screen out the appropriate hazard factors according to the total impact relationship matrix and impact network relationship diagram [
36,
37,
38,
39,
40]. In this study, the DEMATEL method is used to establish the coupling strength of hazard factors. The specific steps are as follows:
Step 1: Analyze the hazard factors of elements’ risk events in the cell grid within a certain time interval, and preliminarily form a list of hazard factors of single element risk events in the grid.
Step 2: Build the direct influence matrix. Let
represent the influence degree of hazard factor
on hazard factor
, while scales 0, 1, 2, 3, and 4 represent no influence, small influence, moderate influence, high influence, and great influence, respectively. According to the work experience of experts, the interdependence degree
of the initially selected hazard factors can be assigned, and the matrix
can be obtained in Equation (6):
Step 3: Establish the direct influence matrix
of hazard factors. Equation (7) is used to normalize the matrix
, and the direct influence matrix
is obtained, as shown in Equation (8):
Step 4: Establish the total relation matrix
of hazard factors. Equation (9) is used to get the total relation matrix, where
was the identity matrix.
Step 5: Solve centrality degree
and cause degree
. See Equations (10) and (11) for
and
, respectively, where,
is any variable in
,
is the sum of rows in the matrix
, and represents the synthesis of the influence of hazard factor
on other hazard factors.
is the centrality, indicating the importance of
relative to other hazard factors.
is cause degree; if
is positive, then the element
is an affecting element; if
is negative, then the element
is an affected element (threshold can be set to ignore indicators with small correlation).
Step 6: Draw a cause-and-effect diagraph. The graph is drawn using as the horizontal axis and as the vertical axis, and the less influential factors are eliminated.
Step 7: Assign the coupling strength of hazard factors. The coupling strength assignment function is established by the sum of rows and columns in the comprehensive influence matrix
, as shown in Equation (12). The coupling strength is used as the input of vulnerability calculation for subsequent risk events.
where,
—Coupling strength of risk event hazard factor in cell grid within a time interval .
—The row sum of the hazard factor in the total relation matrix .
—The column sum of hazard factor in the total relation matrix .
According to the concept of vulnerability, this study puts forward an assignment function of the safety behavior risk vulnerability of employees in a train operation system for the first time. The vulnerability of risk events is obtained by combining the coupling strength of hazard factors with the weight of hazard factors. The function formula is expressed in Equation (13).
where
is the weight coefficient, which satisfies Equation (14).
- (5)
Severity calculation
The occurrence of risk events may cause various consequences, e.g., casualties, property losses, and equipment damage; this study only considers casualties. In the traditional two-dimensional risk matrix, from the perspective of the system, the severity of different risk events can be divided into multiple levels, but when a single determined risk event occurs, the severity of its consequence is unique. Therefore, in the process of risk analysis, this study considers a unique assignment to the consequence of a single risk event in the grid.
- (6)
Risk level calculation
Based on the classification of risk possibility, severity, and vulnerability by the semiquantitative analysis method, the “addition” algorithm is suitable to solve the risk magnitude. When using the traditional two-dimensional matrix to calculate the risk size, the size or magnitude of the risk is usually expressed by the “combination” of the result and its probability. Many scholars generally use the “multiplication” relationship to express this “combination”. The International Organization for Standardization [
29] pointed out that this “combination” relationship did not specifically refer to the product relationship but also the “addition” relationship or other functional relationship. The British Standards Institute [
30] also pointed out that the traditional “multiplication” algorithm for frequency and results might lead to the inaccuracy and inconsistency of the final risk level and recommended the “addition” algorithm.
Based on the aforementioned analysis, if the semiquantitative method is used to calculate the risk magnitude, the “multiplication” algorithm is used for the three parameters, and the calculation error will be greater than that of the “addition” algorithm; therefore, the “addition” algorithm is slightly more accurate in this study (Equation (15)).
where
—the risk event magnitude in cell grid within time interval ;
—the possible magnitude of a risk event;
—the severity of the consequence magnitude of the risk event;
—the vulnerability magnitude of the risk event.