A Risk Characterization Model and Visualization System in Aluminum Production

Abstract

Electrolytic aluminum operation accidents have caused great losses to countries and people. Therefore, taking two typical accidents of explosion and leakage in electrolytic aluminum production as the research object, the form of accident risk characterization was explored and a risk characterization visualization system was designed. Based on the methods of risk assessment and characterization, the likelihood and consequence of accidents were studied. The influencing factors of likelihood and a type of Euclidean distance formula were used to characterize the likelihood. The consequence portion was characterized by two components, with one being the failure degree determined by the accident and the other being the exposure degree of people and equipment. The intensity of event was used to characterize the failure degree and the spatial search model was used to characterize the exposure degree. Finally, the visual system of electrolytic aluminum operation accidents was established based on the risk characterization model.

1. Introduction

High-temperature molten metal operation accidents occur frequently, causing loss of life as well as heavy property losses for the state and people [1,2,3,4]. As a branch of high-temperature molten metal operation, electrolytic aluminum production also faces many safety problems [5,6,7]. China is rich in bauxite resources. According to the report of China’s Ministry of Natural Resources, by the end of 2020, China’s proven bauxite resource reserves (ore) were 57.65 billion tons [8]. In the 21st century, China’s aluminum processing industry has entered a period of rapid development, and the problem of production safety in electrolytic aluminum enterprises has become increasingly prominent. Therefore, the scientific and reasonable characterization of typical accidents such as leakage and explosion in the production of electrolytic aluminum is a key step to ensuring production safety.

Research on risk characterization has already been carried out in relation to natural disasters, public safety, food safety, etc. For example, Cui et al. [9] summarized the current situation of natural disaster research and emphasized cutting-edge scientific problems and scientific challenges, such as the technological gap between natural disasters and the disaster risk disciplines that China would likely face in 2025–2035. Hayes et al. [10] concluded that minimizing the risk to the public from a major gas transmission pipeline or distribution network failure would be better served by the economic regulatory regime, considering safety-related expenditure separately from all other expenditure categories. Domenech et al. [11] presented the rationale, formulation, and application of the probability of exceedance as a metric capable of characterizing public health risks due to exposure to non-threshold chemical hazards in food. However, research on the safety of electrolytic aluminum operation mainly focuses on improving the monitoring system, building a reasonable evaluation system, and solving the control accuracy of the temperature field in the furnace. For example, Neeraj et al. monitored the online state of the aluminum electrolytic capacitor by using artificial neural networks to improve the overall reliability of the system [12]. Xie et al. established a fuzzy comprehensive evaluation index system for electrolytic aluminum production safety to conduct a fuzzy comprehensive evaluation for the production safety of electrolytic aluminum [13]. Tatyana et al. used the mathematical model of spatial distribution to model the temperature field to solve the problem of the experimental determination of internal defects in the bottom of furnaces and studied the control furnace automation system to solve the synthesis problem of the distributed high-precision controller for continuous furnace temperature field control [14,15]. Research on the accident risk characterization of electrolytic aluminum operations focuses on traditional two-dimensional risk characterization models. For example, Chen et al. proposed a double-dimensional classification method of hazards and an evidence-based framework for hazard identification for systematic hazard screening and risk reduction and built a process-oriented hazard evolution and risk control method system [16].

Accident cause theory is an accident mechanism and model extracted from a large number of typical accident analyses. It is the basis of safety science and has a research history of more than 100 years [17]. Up to now, theories of accident causes mainly include accident frequency tendency theory, accident causal chain theory, accident epidemiology method theory, energy accidental release theory, system theory, trajectory crossover theory, two types of hazard source theory, etc. [18,19,20]. Among them, according to the theory of the accidental release of energy, if the control of energy is lost for some reason, the accidental release or escape of energy against people’s will occurs, resulting in the suspension of ongoing activities and, ultimately, accidents [21,22,23]. In the production of electrolytic aluminum, energy does not always produce, convert, and work according to people’s intentions, which may cause human or mechanical damage. In this paper, based on the theory of accidental energy release and the characteristics of four typical accidents of explosion and leakage, the calculation formulas of accidental energy release during the occurrence of two accidents are summarized and the intensity of event is measured and calculated by these formulas. The intensity of event represents the failure degree or intensity determined by the technology itself and is also the basis for determining the scope of the search space.

Risk analysis and evaluation refers to the process of analyzing the nature of accidents that may be caused by hazards, conducting risk evaluations according to the likelihood and consequence of hazards, and determining risk levels [24,25,26]. As an important means of accident prevention and control, risk analysis and evaluation are widely used in the field of industrial production safety. Common methods include Delphi’s technology, HAZOP (hazard and operability study), PHA (preliminary hazard analysis), FMEA (failure mode and effect analysis), and other qualitative methods, as well as the LEC evaluation method, risk matrix, analytic hierarchy process, support vector machine, and quantitative methods of VIKOR and TOPSIS [27,28,29,30]. Most of these traditional risk characterization methods are based on two-dimensional methods such as text, numerical values, formulas, and charts [31]. With the continuous development of the integration of “informatization” and “industrialization”, emerging technologies such as VR show great advantages in industrial production management and have a wide range of applications in machinery manufacturing and other fields. For example, Hu et al. [32] proposed a virtual reality framework to integrate the modeling and simulation of working processes with the visualization of multisource analysis data from various types of computer-aided engineering (CAE) software. Choi et al. [33] proposed a situation-dependent remote AR collaboration approach that can selectively support either image- or live-video-based AR collaborations. Kuo et al. [34] developed a real-time simultaneous localization and mapping (SLAM)-based, virtual reality, three-dimensional, human–machine interaction system to provide users with immersive telepresence to better operate a remote mobile manipulator in an unknown environment. It has also been applied in the field of molten metal. For example, Chen et al. comprehensively considered the possibility, severity, and exposure of safety accidents in electrolytic aluminum production and built a three-dimensional visualization system for hazards and risk characterization [35]. Li et al. described the evolution process of risks based on risk identification and analysis and built a three-dimensional visualization system [36]. However, these studies mainly focus on the three-dimensional visual display of production processes and mechanical equipment and do not well combine the characteristics of typical accidents in the production process for risk characterization, let alone the description of the spatio-temporal characteristics of different accidents. Explosion and leakage accidents are particularly typical in the production process of electrolytic aluminum. A large number of researchers have conducted simulation studies on explosion and leakage accidents [37,38,39]. The method proposed in this paper is similar to accident simulation but different from traditional numerical simulation. Through the physical characteristics of explosion and leakage accidents, a space search model was constructed to determine the severity of accident consequences.

Therefore, we took the traditional risk characterization model as the theoretical basis and studied the likelihood of events, the failure degree determined by the technology, and the consequences of accidents in the risk characterization model. After completing the theoretical research, a visual system for risk characterization was constructed to comprehensively visualize the typical accident risks of electrolytic aluminum operation.

2. Risk Characterization Model

Haddon et al. put forward the theory of accidental energy release; they believed that an accident is an abnormal or unwanted release of energy that is transferred to the human body [40,41]. According to the theory of accidental energy release, the occurrence of accidents occurs in two stages: “energy release” and “energy transfer”. In the first stage, the accidental release of energy causes energy to jump from a reasonable position to an abnormal position. In the second stage, the energy from the abnormal position is transferred to the receptors causing the accident. Combined with risk characteristics, the likelihood of the accidental release of energy to the abnormal position is the likelihood of the event; the transfer of energy from the abnormal position to the receptors determines the degree of exposure.

The energy of the abnormal position is used to describe the degree of failure of the event, called event intensity. Risk is defined as the impact of uncertainty on objectives [42], in which “uncertainty” and “impact” are generally understood as “likelihood” and “consequence” to characterize the risk. However, most methods directly use words to characterize likelihood and consequence when evaluating risk, without further analysis and evaluation, which leads to a lack of a deep understanding of the risk and weak risk control. Therefore, the likelihood of the event is different from the “probability” in mathematical statistics and is often determined by human or material factors. On the other hand, event intensity is often related to its own technical factors, such as the temperature of molten aluminum that determines the explosion energy.

Controlling occupational hazard exposure is the fundamental method to protect workers. Traditionally, a hierarchy of controls has been used as a means of determining how to implement feasible and effective control solutions. Hierarchical control is divided into five levels: elimination, substitution, engineering control, administrative control, and personal protective equipment (PPE) [43]. The hierarchy of controls, the theory of energy accidental release, and risk assessment are combined to build the relationship diagram so as to prepare for effective risk control. Elimination and substitution measures are taken when the energy is in a reasonable position, engineering, and administrative control measures are taken when the energy is accidentally released, and PPE measures are taken when the energy at an abnormal position is transferred to the receptors. The relationship between the hierarchy of controls and risk assessment based on the theory of accidental energy release is shown in Figure 1.

Table 1. Nomenclature.

Nomenclature		NPD	number of deaths caused by accident
A	area of leaking hole, m2	NPI	number of injuries caused by accident
Cex	extent of damage	P	medium pressure in vessel, Pa
C0	specific heat capacity of aluminum, kJ/(kg*k)	P0	ambient atmospheric pressure, Pa
Cw	saturated water blasting energy coefficient, kJ/m3	ΔP	shock wave overpressure, Pa
Cd	discharge coefficient	QTNT	TNT explosion heat, MJ/kg
Cin	intensity of event, kJ	Q	leakage mass flow, kg/s
Eexp	explosion accident event intensity, kJ	Qmax	maximum leakage mass flow, kg/s
Elk	leakage accident event intensity, kJ	Qavg	average leakage mass flow, kg/s
Ew	blasting energy, kJ	Rda	loss risk value of accident
E0	thermal energy of disturbed liquid aluminum, kJ	Rfa	failure risk value of accident
fu	per capita disposable income of urban permanent residents, CNY	r	leakage accident space search radius, m
fr	per capita disposable income of rural permanent residents, CNY	R1	death radius of personnel, m
g	gravitational acceleration, m/s2	R2	serious injury radius of personnel, m
Hmin	minimum liquid layer thickness of liquid pool, m	R3	minor injury radius of personnel, m
h	height difference between liquid level and leaking hole, m	Rd	property damage radius, m
Lo	accident economic loss, CNY	S	area of liquid pool, m2
L	likelihood of accident	t	time of aluminum liquid leakage, s
L,…,Ln	influencing factors of likelihood	tmax	maximum duration of leakage, s
LPD	death converted into economic loss, CNY	t0	molten aluminum temperature, k
LE	economic loss of equipment, CNY	v0	volume of water, m3
LPI	injury converted into economic loss, CNY	va	volume of molten aluminum disturbed, m3
m	quality of leaked molten aluminum, kg	WTNT	TNT equivalent mass, kg
M	quality of liquid aluminum in container, kg	π	circumference
n	number of influencing factors	ρ	density of molten aluminum, kg/m3

contains the nomenclature with descriptions of all the terms covered in this paper.

2.1. Likelihood Characterization Model

Statistical data on molten aluminum accidents in China are scarce; thus, it is difficult to obtain the probability of an event. Therefore, influencing factors are used to characterize the likelihood of an event and the European distance concept is used to calculate the likelihood of an event. This likelihood is different from the statistical probability. Its magnitude reflects the functional uncertainty of technology and equipment or the efficiency uncertainty of personnel and operations and the relative degree of these uncertainties, rather than random uncertainty. Users should pay more attention to how to control the factors to reduce the likelihood of events. The influence factors are different when evaluating the likelihood of different hazards.

The influencing factors are regarded as the coordinate axis value of the n-dimensional space coordinate, and the coordinate origin is regarded as the safety datum point. The likelihood is expressed by 1⁄$\sqrt{n}$ of the Euclidean distance from the origin of an n-dimensional coordinate point composed of the degree of influence of these factors. The likelihood characterization formula is shown in Formula (1):

$$L=\sqrt{L_1^2+L_2^2+\dots L_n^2}/\sqrt{n}$$

(1)

The influencing factors of likelihood are divided into two categories: unsafe behavior of people and unsafe state of objects, as shown in

Table 2. Influencing factors of likelihood.

Dimension	Sub-Dimension	Influencing Factor
Influencing factors of unsafe behavior of people	Safety consciousness	Education level (L1)
		Assessment results of safety training (L2)
	Skill level	Work experience (L3)
		Vocational and technical qualifications (L4)
	Psychosomatic state	Mental health assessment results (L5)
		Occupational health examination (L6)
	Other human factors	Other human factors (L7)
Influencing factors of unsafe state of objects	Nominal mass	Design level (L8)
		Construction quality (L9)
	Technical status	Service effectiveness depreciation (L10)
		Historical fault conditions (L11)
	Maintenance	Inspection and maintenance cycle (L12)
		Inspection and maintenance technology (L13)
	Other factors of objects	Other influencing factors of substances (L14)

. Among the influencing factors of unsafe behavior of people and unsafe state of objects, there are unpredictable factors at the current cognitive level, and these factors also determine likelihood. Accidents caused by these factors are called normal accidents. “Other human factors” was added to the influencing factors of unsafe behavior of people and “Other factors of objects“ was added to the influencing factors of unsafe state of objects to represent the influencing factors that cause normal accidents. The evaluation criteria for influencing factors are shown in

Table 3. Evaluation criteria for influencing factors.

Influencing Factor	Value Range
	(0, 0.33]	(0.33, 0.67]	(0.67, 1)
L1	master	high school to bachelor	middle school
L2	80 and above	60 to 80	below 60
L3	more than 8 years	4–8 years	less than 4 years
L4	senior technician	intermediate technician	junior technician
L5	80 and above	60 to 80	Below 60
L6	good	qualified	unqualified
L7	random assignment in (0, 1)
L8	advanced technology structural safety	general technology general structural safety	backward technology and poor structural safety
L9	meet the design requirements, good quality	meet the design requirements, with average quality	not meeting the design requirements, poor quality
L10	(0, 0.33]	(0.33, 0.67]	(0.67, 1]
L11	[0, 2]	(2, 4]	(4, +∞)
L12	short	commonly	long
L13	automatic detection equipment, advanced technology	need manual assistance detection, technology is general	reliance on manual detection, technology is backward
L14	random assignment in (0, 1)

.

2.2. Intensity of Event Model

Intensity of event represents the failure degree determined by the technology. It is measured by the energy accidentally released in the accident. According to the theory of the accidental release of energy and the characteristics of explosion and leakage accidents, two models of event intensity were summarized. There were some assumptions and reasoning in order to avoid unnecessary tedious calculations.

2.2.1. Intensity of Explosion Accident Model

Most liquid aluminum explosions are a boiling liquid expanding vapor explosion (BLEVE) [44,45]. Therefore, the blasting energy (E_w) and thermal energy of the disturbed liquid aluminum (E₀) constitute the explosive accident event intensity (E_exp).

The blasting energy (E_w) [46]:

$$E_w=C_w{v}_0$$

(2)

The thermal energy of the disturbed liquid aluminum (E₀):

$$E_0=C_0{t}_0\rho v_{\mathrm{a}}$$

(3)

The intensity of event of explosive accident (E_exp):

$$E_{exp}=E_w+E_0=C_w{v}_0+C_0{t}_0\rho v_a$$

(4)

2.2.2. Intensity of Leakage Accident Model

Some scholars use Bernoulli and energy equations to establish leakage judgment mathematical models [47,48,49]. Formula (5) calculates the mass flow rate of molten aluminum leakage:

$$\mathrm{Q}=C_{d}A\rho \sqrt{\frac{2\left(p-p_0\right)}{\rho }+2gh}$$

(5)

The containers that may cause molten aluminum leakage include electrolytic cells, vacuum aluminum ladles, and mixing furnaces. The air pressure inside and outside electrolytic cells and mixing furnaces is almost the same, and normal vacuum aluminum ladles are negative pressure. However, according to the actual investigation, when leakage of a vacuum aluminum ladle occurs, the internal medium pressure of the vacuum aluminum ladle is roughly equal to the external air pressure ($P_0\approx P$, $\frac{2\left(P-P_0\right)}{\rho }\approx 0$); the mass flow rate of molten aluminum leakage can be simplified as Formula (6):

$$Q=C_{d}A\rho \sqrt{2gh}$$

(6)

In the process of leakage, the mass flow rate changes with the change in height difference between the liquid level and leaking hole (h). To facilitate calculation, half of the initial mass flow rate was taken as the average mass flow rate in the whole leakage process, as shown in Formula (7):

$$Q_{avg}=\frac{\mathrm{Q}}{2}=\frac{C_{d}A\rho \sqrt{2gh}}{2}$$

(7)

According to experience, the energy released by molten aluminum leakage is mainly divided into two parts: one is the gravitational potential energy of molten aluminum and the other is the thermal energy of molten aluminum. Since the thermal energy is far greater than the gravitational potential energy, the gravitational potential energy can be ignored. The intensity of event of a leakage accident (E_lk) is shown in Formula (8):

$$E_{lk}=t_0{C}_0{\mathrm{Q}}_{avg}t=\frac{{t{t}_0{C}_{0}C}_{d}A\rho \sqrt{2gh}}{2}$$

(8)

2.3. Spatial Search Model

In electrolytic aluminum operation accidents, receptors refer to objects that are exposed to harm, such as personnel, equipment, etc. The spatial search method is used to determine the impact range of the accident through the accidental release intensity of energy and the characteristics of the accident and search the people and equipment within the impact range in the visualization system. In the system, the receptors exposed to the impact range are searched based on spatial distance and physical collision. Before using the spatial search function, relevant information on personnel and equipment (type of work, space location, protection status, type of equipment, size of equipment, and so on) should be embedded in the system according to the actual production situation of electrolytic aluminum operation.

2.3.1. Space Search Model of Explosion Accident

For an explosion accident, the system first calculates the accidental release of energy, then converts the accidental energy release into a TNT equivalent. The damage range was determined according to the TNT equivalent. The exposed people and equipment were obtained through a space search according to the damage range [50,51]. Formula (10) gives the TNT equivalent:

$$W_{TNT}=\frac{E_{exp}}{{\mathrm{Q}}_{TNT}}$$

(9)

In order to estimate the possible casualties caused by explosion accidents, the scope of personal injury caused by explosion accidents is usually divided into three areas (death, serious injury, and minor injury). The accidental release of energy also causes great damage to surrounding structures. Thus, the property loss radius R_d is introduced, which indicates the range of secondary damage to buildings under the action of an explosion shock wave.

(1)

Death

If there are no protective measures, few people will survive within this range, and the death radius is recorded as R₁. The calculation formula is as follows:

$$R_1=13.6{\left(\frac{W_{TNT}}{1000}\right)}^{0.37}$$

(10)

(2)

Serious injury

If there are no protective measures for personnel, the personnel in the area are likely to be seriously injured, with only a few slightly injured. The radius of serious injury is recorded as R₂, which requires that the peak overpressure of the shock wave is 44 kPa. The radius of serious injury can be calculated according to the overpressure value, as shown in the following formula:

$$△\mathrm{P}=0.137Z^{-3}+0.119Z^{-2}+0.267Z^{-1}-0.019$$

(11)

$$\mathrm{Z}=R_2{\left(\frac{P_0}{E}\right)}^{\frac{1}{3}}$$

(12)

$$△\mathrm{P}=\frac{44000}{P_0}$$

(13)

(3)

Minor injury

This area has little impact on people, most of whom are only slightly injured and rarely die. The minor injury radius is R₃ and the required peak overpressure of the shock wave is 17 kPa. The minor injury radius can be calculated according to the overpressure value, as shown in the following formula:

$$△\mathrm{P}=0.137Z^{-3}+0.119Z^{-2}+0.267Z^{-1}-0.019$$

(14)

$$\mathrm{Z}=R_3{\left(\frac{P_0}{E}\right)}^{\frac{1}{3}}$$

(15)

$$△\mathrm{P}=\frac{17000}{P_0}$$

(16)

(4)

Equipment and property loss

The accidental release of energy also causes great damage to surrounding structures. Therefore, the property loss radius R_d is introduced, which indicates the range of secondary damage to buildings under the action of an explosion shock wave. According to the overpressure impulse criterion, the property loss radius R_d is calculated according to the following formula:

$$R_d=\frac{4.6W_{TNT}^{\frac{1}{3}}}{{\left[1+{\left(\frac{3175}{W_{TNT}}\right)}^2\right]}^{\frac{1}{6}}}$$

(17)

2.3.2. Space Search Model of Leakage Accident

According to Formula (7), the maximum duration of leakage can be calculated as follows:

$$t_{max}=\frac{\mathrm{M}}{Q_{avg}}$$

(18)

The mass of leaked molten aluminum is as below:

$$\mathrm{m}=Q_{avg}\mathrm{t}$$

(19)

The relationship between the liquid pool area and the minimum liquid layer thickness is as follows [52]:

$$\mathrm{S}=\frac{\mathrm{m}}{H_{min}\rho }=\frac{Q_{avg}\mathrm{t}}{H_{min}\rho }$$

(20)

The minimum liquid layer thickness is determined according to the ground type of the electrolytic aluminum plant. In the system, a circle is used as the shape of the leakage liquid pool; the search radius is Formula (22):

$$\mathrm{r}={\left(\frac{S}{\pi }\right)}^{\frac{1}{2}}={\left(\frac{Q_{avg}\mathrm{t}}{H_{min}\rho \pi }\right)}^{\frac{1}{2}}$$

(21)

Due to the high energy density of molten aluminum leaked and the timeliness of leakage, and taking into account the subjective initiative of personnel, it is assumed that in a leakage accident, personnel will not be injured when evacuating the leakage area and all the equipment searched in the liquid pool will be damaged.

2.4. Accident Risk Characterization

2.4.1. Economic Loss Model of Exposure

Personnel and equipment are searched according to the spatial search model, and the accident economic model of Liu et al. is used to convert the exposure of the accident into economic losses [53]. At present, there are no strict national laws and regulations on accident compensation standards. Through the per capita income level, combined with the economic development level of each province, according to the life and health value analysis theory in safety economics, the calculation model of economic loss of typical electrolytic aluminum accidents is obtained.

$$L=L_{PD}{N}_{PD}+L_{PI}{N}_{PI}+L_E$$

(22)

$$L_{PD}=20\times \frac{\left(f_u+f_r\right)}{2}$$

(23)

$$L_{PI}=0.5L_{PD}$$

(24)

2.4.2. Risk Value

The likelihood reflects the functional uncertainty of technology and equipment or the efficiency uncertainty of personnel and operation. The intensity of event, which is the failure degree determined by the technology, is described by the energy released accidentally. In the visualization system, the method of spatial search is used to determine the degree of exposure of an accident.

The degree of exposure changes, but the intensity of event does not. This study proposed two methods to characterize the risk value. One was to use the product of likelihood and degree of exposure to characterize the risk of damage of accident, which will change with the change in time and space, characterizing the randomness and unpredictability of the accident, as shown in Formula (25). In the other, the product of likelihood and intensity of event are used to characterize the risk of failure of accident, which does not change with time and space, characterizing the orderliness and controllability in risk control, as shown in Formula (26).

$$R_{da}=L\times C_{in}$$

(25)

$$R_{fa}=L\times C_{ex}$$

(26)

3. Risk Characterization System

3.1. System Design

3.1.1. Overall Architecture Design

The overall architecture design of the system is shown in Figure 2, including data, algorithm, and application layers. The data layer mainly includes the hazard event database, parameter description table, accident chain database, and device model database. The algorithm layer includes the likelihood characterization algorithm, event intensity characterization algorithm, spatial search algorithm, and risk assessment algorithm. The application layer includes hazard identification, risk characterization, overall roaming, and accident rehearsal. Two system versions (desktop PC and VR headsets) were designed to increase the immersive experience of users.

3.1.2. Operating Process Design

Figure 3 is the operating process chart. This process consists of several steps: entering the system through identity authentication; selecting the process; entering the preset hazard of the workplace to identify the hazard; entering the safety production visualization; selecting the likelihood influencing factors, intensity of event parameters, and spatial search parameters; obtaining the personnel and equipment within the exposure range; and entering other process links or exiting the system.

3.1.3. Hazard Safety Signs

The identification of hazards is a necessary part of risk characterization. To better characterize hazards, the concept of the hazard safety sign is introduced here. Hazard safety signs refer to the visualization of hazards described by language to highlight the internal nature of hazards, give people a visual impression and memory of them in a short time, and enrich the content of hazard characterization. According to research on typical hazards of electrolytic aluminum production, hazards are divided into 12 categories according to the unsafe behavior of people and the unsafe state of objects, and hazard safety signs are designed according to these 12 categories of hazards.

Hazard safety signs can be used to remind relevant personnel of hazards and risks of accidents; improve safety, risk, and emergency response awareness; and help to resolve risks and reduce accident hazards. They can be of particular use in the system. However, at present, there is no relevant hazard safety sign design available in the industry. Therefore, a complete set of hazard safety signs (12 black labels on a yellow background) was designed according to the classification of accident hazards, which mainly takes equipment, operation scenarios, and ergonomics as the basic elements, and refers to typical hazard scenarios as the scenario framework of sign design. The hazard safety signs are shown in Figure 4.

3.2. Application of System

3.2.1. Hazards and Receptor Settings

Based on virtual reality technology, the system took explosion and leakage accidents as the object and carried out three-dimensional modeling through 3DMax, CAD, three-dimensional laser scanning, and other modeling technologies. A visualization system was developed by using Unity3d+C#.

Starting from the evidence of standards, specifications, scientific and technological literature, and accident cases, for the explosion and leakage accidents of electrolytic aluminum operation, according to the operation scene of the electrolytic workshop, vacuum aluminum ladle, and foundry workshop sections, hazards of accidents were identified and buried in the exact spatial position of the visualization system.

In an electrolytic aluminum operation accident, the receptor refers to the object that directly bears the consequences of the event, such as personnel, equipment, etc. The exposure of the receptor refers to the number of people or devices exposed in the search space. The severity of the consequences of the incident is defined by the exposure of people or equipment in the search space. Before the use of the spatial search function, it is necessary to refer to the actual production situation of electrolytic aluminum operation and bury relevant information such as the type of work, spatial location, protection state and type of operator, and size of equipment used in the system. After that, the intensity of the event can be obtained through the selection of parameters in the system, and the spatial search scope can be determined according to the intensity of the event to identify the people and equipment exposed in the search space. Some references for building the system are shown in

Table 4. References for building the system.

Serial Number	Title
1	Safety specification for aluminium electrolysis (GB 29741–2013)
2	Code for design of aluminum smelter processes (GB 50850–2013)
3	Code for design of shutting down/restarting aluminum reduction cells without power interruption (GB 51010–2014)
4	Du, K., Chai, Y., et al., Aluminum electrolysis and Aluminum alloy Casting Production and Safety [M]. Beijing: Metallurgical Industry Press, 2012.
5	Shi, M., Simulation Training of Electrolytic Aluminum Production [M]. Guiyang: Guizhou Science and Technology Press, 2016.
6	Shen, Z., Evaluation of Explosion Effect of Heavy Molten Aluminum on Water [J]. Industrial Safety and Environmental Protection, 2020.
7	Gao, W., Safety Production Management of Electrolytic Aluminum Industry [J]. Labor Protection, 2011.
8	Zhou, N., Hu, B., et al., A kind of embedded high-temperature molten metal leakage recovery tank: China, 201910135140.2 [P]. 2019-02-22.
9	Chen, B., Shi, X., et al., A ground-lift high temperature molten metal leakage barrier device: China, 201811274313.0 [P]. 2018-10-30.
10	Zhang, X., Leakage and prevention of electrolytic cell [J]. China Chlor-Alkali, 2001.
11	In August 2007, Shandong Province, the aluminum spilled into the chute. The energy gathered and exploded, killing 20 people and seriously injuring 59.
12	On 28 August 2018, an aluminum company in Jiangyin City dumped a large amount of liquid aluminum on the casting plate instantly into the cooling water. The high-temperature liquid aluminum reacted violently with the cooling water, forming a violent steam explosion, causing 5 serious injuries and 27 minor injuries.

.

3.2.2. Explosion Accident Risk Analysis

(1) Likelihood of Explosion Accident

Taking the explosion accident in the electrolytic section as an example, there is a hazard of “insufficient preheating of tools” in a certain scenario. This hazard belongs to the unsafe behavior of people, selecting L₁, L₂, L₃, L₄, L₅, L₆, and L₇ as the influencing factors to describe the likelihood. The possible influencing factors were assigned according to the production process and Table 2. The likelihood influencing factors and their assignment are shown in

Table 5. Likelihood influencing factors and their assignment.

Influencing Factors	Assignment
Education level (L1)	0.2
Assessment results of safety training (L2)	0.1
Work experience (L3)	0.4
Vocational and technical qualifications (L4)	0.1
Mental health assessment results (L5)	0.15
Occupational health examination (L6)	0.15
Other human factors (L7)	0.528

, according to Formula (1), L ≈ 0.2787.

(2) Consequence of Explosion Accident

According to the actual production situation of the electrolysis workshop, the parameter assignment of an explosion accident event intensity can be obtained, as shown in

Table 6. Event intensity parameter assignment.

Parameter	Assignment
Saturated water blasting energy coefficient, Cw (kJ/m3)	3 × 104
Volume of water, v0 (m3)	0.2
Specific heat capacity of aluminum, C0 (kJ/(kg*k))	0.956
Molten aluminum temperature, t0 (k)	1000
Density of molten aluminum, t0 (kg/m3)	2.37 × 103
Volume of molten aluminum disturbed, ${\rho }_a$ (m3)	0.4
TNT explosion heat, QTNT (MJ/kg)	4.52
Ambient atmospheric pressure, P0 (Pa)	1.01 × 105

. According to Formula (4), E_exp ≈ 912288 KJ, and according to Formula (27), R_fa = L × C_in = 0.2787 × 912288 ≈ 254254 KJ (in this case, the energy accidentally released from an explosive accident (E_exp) is used to characterize the event intensity (C_in)). According to Formulas (11), (13), (16), and (18), R₁ ≈ 7.5 m, R₂ ≈ 11.5 m, R₃ ≈ 66.5 m, and R_d ≈ 10.8 m, respectively.

3.2.3. Risk Value of Explosion Accident

Based on the space search range obtained from the above calculation, the number of exposed persons was 10 (2 deaths, 3 serious injuries, and 5 minor injuries) and the number of exposed pieces of equipment was 7 (1 vacuum aluminum ladle, 1 ladle car, 1 multi-functional crane, 1 workshop, and 3 electrolytic cells). According to the parameter assignment of the accident economic model as shown in

Table 7. Parameter values of accident economic model.

Economic Model Parameters	Value (Ten Thousand RMB)
Per capita disposable income of rural permanent residents ($f_r$)	1.89
Per capita disposable income of urban residents ($f_u$)	4.74

, the equipment value as shown in

Table 8. Equipment value.

Equipment Name	Value (Ten Thousand RMB)
Bag carrier	25
Electric tank	45
Electrolytic workshop building	20
Multi-function crane	50
Vacuum aluminum tapping and ladle lifting	18

, and the accident economic characterization model, C_ex ≈ 6.458 million CNY, and then according to Formula (26), R_da = L × C_ex = 0.2787 × 645.8 ≈ 1.8 million CNY (in this case, the economic loss caused by an explosion accident is used to characterize the degree of damage (C_ex)).

4. Discussion

(1) In traditional risk characterization methods [31], historical accidents are often used to statistically predict. Data on molten aluminum accidents are scarce so it is difficult to obtain the likelihood of an accident using statistics. Thus, influencing factors were used to characterize the likelihood of events. Likelihood is different from statistical likelihood; it reflects the functional uncertainty of technology and equipment or the efficiency uncertainty of personnel and operations as well as the relative degree of these uncertainties, rather than random uncertainties. Fourteen influencing factors were selected and a formula similar to the Euler distance formula was used to characterize the size of the likelihood. It should be noted that the influencing factors were not fixed but were selected according to the production situation. The formula was chosen because it can reasonably describe the space distance between high-dimensional space coordinate points composed of likelihood factors and safety reference points (coordinate origins), and it is a method to reasonably measure the degree of deviation between high-dimensional space coordinate points composed of likelihood factors and coordinate origins. Compared with arithmetic mean value, this method pays more attention to the differences among influencing factors. For example, in two-dimensional space:

$$\sqrt{{\left(\frac{x_1+x_2}{2}\right)}^2+{\left(\frac{x_1-x_2}{2}\right)}^2}=\sqrt{\frac{x_1^2+x_2^2}{2}}\ge \sqrt{{\left(\frac{x_1+x_2}{2}\right)}^2}=\left|\frac{x_1+x_2}{2}\right|$$

where ${\left(\frac{x_1-x_2}{2}\right)}^2\ge 0$ if and only if $x_1=x_2$ is equal; this inequality means that in the case of two parameters when the absolute values of the arithmetic mean of the parameters are the same, the greater the difference between the values of the influencing factors of likelihood and the greater the likelihood of the accident.

(2) Compared with traditional risk characterization methods [31], the concept of intensity of event was proposed, which characterized the failure degree determined by the technology. Based on the theory of accidental energy release, using the energy accidentally released in the accident to characterize the event intensity, the concept of risk of failure was proposed to represent the impact of uncertainty on the degree of failure of accidents. Risk of failure had nothing to do with time and space, and its size could be changed by controlling influencing factors of likelihood and parameters of intensity of event. Therefore, risk of failure described the orderliness and controllability of risk control from another perspective. The method of spatial search is to search for personnel and equipment within the scope of the accident in the visualization system to characterize the degree of exposure. Of course, the degree of exposure can be converted into economic losses through the economic loss model. Formula (26) is used to represent the risk of damage, which represents the impact of uncertainty on the damage of exposure. Due to the uncertainty of the location of accidents and receptors in the exposure, the risk of damage will change with time and space, which shows the randomness and unpredictability of accidents.

(3) There are many methods of risk assessment.

Table 9. Applicability of tools used for risk assessment.

Tools and Techniques	Risk Assessment Process					Risk Characterization Effect
	Risk Identification	Risk Analysis			Risk Evaluation
		Consequence	Probability	Level of Risk
Brainstorming	SA	NA	NA	NA	NA	Can only be used to identify hazards
Checklists	SA	NA	NA	NA	NA	Can only be used to identify hazards
Consequence/probability matrix	SA	SA	SA	SA	A	The risk level can be obtained and a two-dimensional risk matrix can be formed
Likelihood/exposure/consequence	SA	SA	SA	SA	SA	The risk level can be obtained and a three-dimensional risk matrix can be formed
Fault tree analysis	A	NA	SA	A	A	Causal factors are deductively identified, organized in a logical manner, and represented pictorially in a tree diagram that depicts causal factors and their logical relationship to the top event
Event tree analysis	A	SA	A	A	NA	A graphical technique for representing the mutually exclusive sequences of events following an initiating event, according to the functioning/not functioning of the various systems designed to mitigate their consequences
Bow tie analysis	NA	A	SA	SA	A	Bow tie analysis is a simple diagrammatic way of describing and analyzing the pathways of a risk from causes to consequences
Spatial search method (this research)	SA	SA	SA	SA	SA	In the system, the impact range of the accident can be visualized in three dimensions and the corresponding risk value can be obtained

SA—Strongly applicable; A—Applicable; NA—Not applicable.

lists some commonly used methods of risk assessment for comparison with the methods in this paper. The content of the comparison is a description of each step of the risk assessment process (risk identification, risk analysis, risk evaluation) and the degree of risk characterization. For each step in the risk assessment process, the application of the method is described as strongly applicable, applicable, or not applicable. One of the additional risks arising from the production of aluminum is the risk of pollution of water resources, including deep-seated pollution. The modeling of such risks, as well as the movement of aquifers, can be found in [54].

(4) At present, most of the visual systems built in industrial safety management are monitoring and early warning systems, which use sensors to monitor the status of the production process in real-time and set thresholds for early warnings. The focus of such systems is to check the failure location and failure tendency in the production process, and the visualization degree is mostly in the form of two-dimensional charts and other forms. Figure 5 shows the real-time monitoring and early warning system of a coal mine roof separation. In the risk characterization visualization system, traditional risk assessment methods are often directly embedded to make a simple visual display without further integration of computer technology. Figure 6 shows the steel production visualization system designed with traditional risk assessment methods, the core of which is the LEC risk assessment method. By referring to traditional risk characterization methods, this study attempts to explore a new type of risk characterization method under the condition of computer technology. The risk value calculated by this method is not completely random, but fully considers the risk value obtained by time, space, and operation process. Because the above three factors are taken into account, the risk value in different times and spaces is different. It is a dynamic risk value. Figure 7 shows the typical accident risk characterization visualization system of electrolytic aluminum operation.

5. Conclusions

Using a structured methodology, the likelihood portion of risk was characterized by human competence and equipment fit for purpose, rather than the usual approach of statistical probability, which is rarely available in the case of occupational accidents. On the other hand, the consequence portion of risk was characterized by two components, with one being the intensity of event determined by technical factors and the other being the exposure to event determined by spatial search range and time and place of the event. This risk characterization model provided convenience and a new direction for quantitative risk assessment and control. This structured methodology of risk assessment is also suitable for industries with few accidents for which it is difficult to form statistical predictions, such as the steel industry.

The visualization system reproduced typical accident simulation scenarios of electrolytic aluminum production and revealed the safety principle in multi-source coupling risk. Hazard safety signs were designed to be used in the visualization system. The signs remind people of the hazards of accidents, improve awareness of emergencies, and help to reduce losses. The system not only provided a new method for the risk characterization of electrolytic aluminum production accidents but also provided a good learning platform for employees, which is of great significance to the safety education and training of the electrolytic aluminum industry.