The 3D-Dynamic Fire Risk Evaluation Method of Modern Logistics Warehouses: A Modified Gustav Method

Abstract

International trade connections with COVID-19 impeding the development of the logistics industry in express delivery, the world has become an inseparable part of daily life. To improve protection competency, there is a need for effective research on logistics warehouse fire accident alarms. The goal of this study is to create a novel fire risk evaluation method for fire safety managers in logistics warehouses. The Gustav method is used to convert a plane model to a stereoscopic model. Hazards to construction, hazards to life, and fire rescue competency are all taken into account. The empirical study used JingDong Gu’an logistics park as a case study, and the evaluation results revealed differences in fire risk levels between the two warehouses. The results show that the transmit warehouse had a higher fire risk level than the sorting warehouse. The method describes the total risk of a warehouse fire. It is appropriate for the various types and processes found in modern logistics warehouses. The results of the developed 3D-Dynamic method demonstrate the model’s feasibility and practicability even to laypeople with limited professional knowledge.

Introduction

COVID-19 has increased demand for the logistics industry, which benefits human society economically. Various news outlets, however, show that logistics warehouse fires generally result in greater economic losses and casualties. In 2016, the Jindong Gu’an logistics warehouse fire accident [1], in Hebei province, China, lost at least 1 billion RMB (more than $15 million). In 2017, Amazon UK logistics warehouse (BHX1) fire accident [2] destroyed more than 1.7 million kinds of goods in one night. In 2018, a transportation logistics warehouse located at Yokosuka, Kanagawa Prefecture, Japan, fired more than 13 thousand square meters [3]. In 2021, Amazon American logistics center warehouse (TEB6), the largest building in New Jersey, drowned in flames [4]. In 3 months later, 38 lives were lost in the fire accident of an underground logistics warehouse in Icheon, Gyeonggi Province, Korea [5]. The growing number of fires in logistics warehouses has prompted people to consider how to improve fire protection competency more quickly.

Modern Logistics Warehouses and Their Fire Risk

Why and what causes frequent fires in logistic infrastructure? The reasons should be considered from both explicit and implicit risks, which correspond to specific fire sources. The characteristics of the logistics industry and fire accidents may indicate the former.

Characteristics of Logistics Industry

Storage, transfer, sorting, processing, and distribution are all components of modern logistics. Logistics warehouses are larger and higher than traditional ones to meet the urgent demand for express deliveries, heavier load-capacity, multi-functional, and automatic to meet the requirements of ‘light-speed delivery’ and ‘zero storage’. Using statistical data, some Japanese scholars compared the fire load density of all construction categories. Table 1 showed that fire loads in warehouses ranked first, with modern logistics warehouse characteristics contributing to an increase in fire probability.

Table 1.

Comparison of Fire Loads Density in Different Constructions in Japan [6]

Occupation	Density of fire load (MJ/m2)	Maximum value (MJ/m2)
Resident building	644–662	1104
Hotel	276–552	552
Meeting room	368–644	644
Designing room	552–2208	2760
Library	1840–4600	4600
Warehouse	3680–18,400	–
Shopping mall	–	1840–3680

Hazards of Logistics Warehouse Fires

Fire features are the clues of fire risks. We summarized fire features according to fire accidents happened from 2005 to 2020, collecting with their complete information and investigation reports. Fire accidents of logistics warehouses generally destroyed large areas, produced poisonous gases, spread rapidly, and led to the collapse of the warehouses.

Research Review of Fire Protection

The logistics industry began in 1965, when Japan built the first logistics park. However, a fire occurred several months later, killing 19 firefighters and injuring 89 others [7]. The processing plant of a logistics park in southern Germany exploded in 1978, causing the most serious fire accident in Germany in the previous decade. During the early years of the logistics industry, fires heightened awareness of the importance of fire protection in logistics warehouses.

The Fire Protection Planning of Logistics Park

Scientific fire safety construction distance was considered as a possible way to decrease fire risk at first. Melendez et al. [8], Dai [9], Shea [10] and Shanfeng [11] suggested the different optimization plans. Expanding the distance from one warehouse to another one was an efficient method to avoid external fire spread at the original developing stage of logistics warehouses. However, only scientific construction distance is not enough to prevent the warehouse fire from occurring with the various functions of modern logistics warehouses.

Standards for Fire Protection

Countries published laws or regulations to standardize the fire protection design for logistics warehouses. For example, the NFPA 230 Standard for the Fire Protection of Storage [12] ruled how to store the inflammable substance outside. The American Building Code [13] classified logistics warehouses into two levels, while the Canadian National Building Code [14] into three. In China, there are special regulations for logistics parks and warehouses, the Classification and Requirement of Logistics Park (GB/T 24,358–2008) [15] as an example. But the regulations hysteric the development of warehouses. Wenhui Ju [16] chose nine typical logistics warehouses in China and studied on the contradictions between standards and demands and optimized fire protection investment strategy. As a result, in order to adapt to the development of the logistics industry, performance-based fire protection designs, rather than the prescriptive approach, became prevalent in order to meet the overall goal of the fire protection requirement.

Performance-Based Design and Insurance

How to balance the fire safe and development? Performance-based design and economic compensation worked it. Performance-based design (PBD) stimulates the development of logistics industry to some extent, as the key to achieve an appropriate level of safety under the type of operations running there. Yumin Tian [17] used methods from the economics of fire protection [18], such as cost–benefit model, to study the optimized Performance-based design (PBD). However, some owners only focus on the fixed fire extinguishing equipment such as fire hydrant system and automatic fire alarm system, ignoring the fire risk management such as firefighting training and rescue drills. It was necessary to develop a fire risk assessment method with management parameters.

Some scholars [19, 20] also studied on risk management, such as fire insurance, to evaluate risk exposure and diversify fire risk. However, insurance is not a cure-all. Fire results in a loss for either stakeholders or the social-economic system. Meanwhile, no insurer is willing to underwrite a risky subject. The cognition and management of fire risk became a significant issue.

Performance-based design isn’t a matter, but the ignoration of the fire risk management, such as firefighting training and rescue drills, also implicitly increases the probability of fire. Therefore, it was necessary to develop a fire risk assessment method containing management parameters.

Fire Risk Evaluation and the Gustav Method

How to value the fire risk of the logistics warehouse? The intuition drove researchers to study on fire risk factors [21, 22] and fire risk characteristics [23]. With comprehensive risk analysis, fire risk evaluation is a common way to value the hazards. There are various assessment methods, including the Fire Risk Model (FRM) [24], J-value [25], index systems [26, 27], and fuzzy comprehensive method [28–30].

Comparing the evaluation components between different methods, the Gustav method includes both property and life hazards, which is consistent with the fire characteristics of logistics warehouses. The application of the Gustav method is multiple, approximately classified into three ways that combination of evaluation methods [31, 32], changing parameters [33], or algorithm [33, 34]. However, these methods put out a stationary fire risk level, overlapping the extreme values, underestimating, or overestimating the cost of fire economics. Therefore, a dynamic fire evaluation method of logistics warehouse is needed.

Research Structure

The studies we reviewed, as promising as they are, necessitate further investigation. While existing fire risk evaluation methods can produce accurate but stationary results, it remains to be seen whether dynamic risk parameters have a significant impact on the fluctuation of fire risk. Notwithstanding these concerns, the literature review indicates that fire risk evaluation is still an efficient way to cognit and distinguish fire risks in logistics warehouse. Although the practices of the Gustav method are not quite suitable to evaluate the dynamic fire risk, its superior characteristics, simple procedures and results, still attract us.

Considering research goals and available resources, we chose the Gustav method in the end. The research goal is to develop a concise method for grassroots safety managers to describe the fluctuation of fire risk, focusing less on how accurate the outcome, because users pay more attention to whether the probability of fire risk is 0.1 or 0.8, not 0.8 or 0.823. And the lack of logistics fire data excludes quantitative methods, because of the early stage of the logistics industry in China. Also, because of the flexible combination of fire risk factors, the Gustav method may realize the image of dynamic fire risk evaluation for logistics warehouses.

The structure is illustrated as follows, as is shown in Fig. 1. Section 1 mainly illustrates the research background and research review, as what you have read. Section 2 is the fire risk analysis, including the fire risk cognition, extraction of dynamic parameters and weighing parameters in the fire risk evaluation index system. Section 3 introduces the 3D-Dynamic fire risk assessment method from four subsections, modified Gustav method, formula, classification of risk level, and instruction. Section 4 shows the empirical study, and we chose two different logistics warehouse types and evaluated their dynamic fire risk. Section 5 concludes this the research. Reference and appendixes will follow.

Figure 1.

Research structure

Fire Risk Analysis of Modern Logistics Warehouses

Modern logistics warehouses are not the traditional ones, the implicit fire risks are more complex. Because logistics warehouses derived various types defined by height, location, and occupation, the hidden fire risks depend on special context, like types and functions of logistics warehouses. Meanwhile, dynamic factors implicit extreme risk values which may cause the ‘Black Swan Event’. However, not all dynamic factors affect fire risk, for example, the weather. Therefore, it’s necessary to extract dynamic parameters then, as well as weigh them.

Heterogenous Analysis of Fire Risk

We chose three classic warehouse types, including storage warehouse, sorting center warehouse, and transmit warehouse, consistent with three main functions of the logistics chain. And the heterogenous analysis was summarized in Table 2.

Table 2.

The Heterogenous Analysis of Fire Risks in Three Warehouse Types

Type	Function	Transportation period	Fire risks	Reasons
Storing warehouse	Storage	More than one week	Large fire loads	•••The capacity of logistics warehouses is 5–10 times that of normal warehouses to satisfy the express need
			Various combustibles	•••Besides general commodities, there are plastic, cotton, linen, rubber products and even lubricating oil
			Dynamic contributions of goods	•••The high frequency of goods flow makes some combustibles accumulate heat out of control
			Hidden ignition points	•••The height of shelves is over the efficient detect distance of automatic fire detectors and sprayers, especially when detecting the corner ignition points
			Electrical failures	•••The electrical or batteries failures are larger proportions of fire reasons
Sorting center warehouse	Storage, Sorting & Manufacturing	2–4 h	Unpredictable fire loads	•••The residence period of goods depends on orders, making it difficult to accurately predict the amplitude of the fluctuation values of fire loads
			High-frequency electrical failure	•••The large-scale automatic equipment leads to an unbalanced contribution of electricity. And electrical failure is the highest fire reason
			High-temperature processing conditions	•••The goods processed by thermoplastic have high-temperature external surfaces, which ignite the combustibles near
Transmit warehouse	Storage & Sorting	Two days or one week	Reduced vigilance	•••The middle storing period relax the vigilance of workers and elevates the group loafing
			Inevitable unsafety behaviors	•••As the fast flow of workers makes the security check loose, arsons or smokers may fire the warehouse easily

Some regulations cover or shall cover this fire risk if properly applied. Why do these risks exist? Most of these problems are because of the failure of risk management.

For example, a modern logistics warehouse should be built with a proper sprinkler design according to the Code for design of sprinkler system (GB 50,084–2017), including ceiling sprinklers and in-rack sprinklers. However, investigations and fire accident reports of several modern logistics warehouses in China showed that it was quite difficult to detect the lowest corner ignition points, such as the ‘Hidden ignition points’.

The fire detection failure of sprinkler systems mainly results from the risk management failure separated into two cases. One is the failure of automatic fire detectors and sprayers. Owners don’t want to spend more on fire protection once passing the fire audit and inspection. Therefore, fire safety managers don’t inspect or maintain the fire protection systems promptly [35]. Sprayers, near the ignition point, cannot detect fire signals.

The other one is the incorrect placement of goods. To realize the maximum cost–benefit value of the operation, users or workers would like to store as many interests as possible per square, which leads to overload. Some inflammable goods, such as cotton and fiber, smolder easily, especially when stored crowdedly in the corner [36]. These ignition points are too hidden to be detected as soon as possible.

In addition, the regulations always lag behind the development of logistics warehouses even though they standardize fire protection design and cover most fire risks. For example, the Code for design of sprinkler system (GB 50,084–2017) only requires the efficient detect distance of automatic fire detectors and sprayers, as well as the rules of storing categories, but no requirement of store location or strategy.

As the essential function in the modern logistics supply chain, storage still occupies most of the construction area, whichever the warehouse-type is, as is shown in Fig. 2a. The sorting center warehouse is also called the ‘Zero storage’ warehouse, the popular type in logistics park, selecting goods from address A to transport to address B with high flow speed. And it is multi-functional, including storing and sorting while the store function is auxiliary. Sorting not only classify goods but produce, for example, packing, unpacking, and thermal process. Generally, besides storing, the sorting center warehouse includes the sorting area and manufacturing area, as is shown in Fig. 2b and c respectively. Transmit warehouse has a longer transportation period than the sorting center warehouse, as is shown in Fig. 2d, while its sorting function is auxiliary on the contrary.

Figure 2.

The insight of modern logistics warehouse. (a) storing warehouse; (b) sorting area of the sorting center warehouse; (c) manufacturing area of the sorting center; (d) transit warehouse

We analyzed the special characteristics using fire accidents, Event Tree Analysis (ETA), and Fault Tree Analysis (FTA). Wenhui Ju [37] innovated the Event and Fault Tree Analysis method (EFTA) to explore the fire spread mechanism of various cotton logistics warehouses and obtained straightly the reducing or protection factors.

Dynamic Parameters Analysis

The analyses of explicit risks in Sect. 1 and implicit ones above extract the dynamic fire risk parameters, as shown in Fig. 3. We also found that some parameters in the original formulas of the Gustav method were parts of dynamic ones.

Figure 3.

Dynamic parameters in logistics warehouses and their correlations

There are two circles. The circle inside includes the main dynamic factors depending on warehouse type, and the ellipse shows the dynamic sub-factors depending on specific factors. We should mention that the correlations between factors and sub-factors are not fixed or unique. The figure describes that some dynamic sub-factors are significant in a factor.

Fire Risk Evaluation Index System

A thorough fire risk analysis provided a solid foundation for developing a fire risk evaluation method. However, the investigation was not conducted in a systematic manner. Furthermore, the judgment of fire risk status quo and evaluation of each parameter from different assessors would make a big noise to the assessment of fire risk level. And the noise might magnify the stochastic error. Index system is an efficient tool to integrate risk parameters and reduce the error.

Wenhui et al. [38] constructed an index system of fire risk evaluation for modern logistics warehouse with four parameters in first level, 10 in second level, and 32 in third level with four noteworthy points (B₂, C₂₇, B₅, and C₃₂), as is shown in Fig. 4. They also weighted parameters by the AHP method and the Delphi method. We use these weighted values as the coefficients of risk parameters in this novel fire risk evaluation method, and more details are listed in Appendix 1.

Figure 4.

The fire risk evaluation index system of modernized logistics warehouses [38]

The 3D-Dynamic Fire Risk Evaluation Method

According to the fixable result of the fire risk level, the traditional Gustav method provides assessors with simple and feasible fire protection plans. Based on the current state of modern logistics warehouses and fire risk characteristics, the traditional version must be modified to be a flexible evaluation method for calculating dynamic fire risks.

The Construction of 3D Gustav Method

The Gustav method, a half-quantitative fire assessment method, classifies fire risk factors into two aspects, the risk to construction’s destroys donated as GR, and the risk to the properties and lives donated as IR. Each point in a rectangular coordinate system composes of GR as the x-axis and IR as the y-axis can determine the fire risk of one building. The planar defined by the original Gustav method is separated into four parts, suggesting four fire protection ways respectively for the users, including the zone without fire protection measure, the zone with automatic firefighting measures, the zone with automatic fire alarm system, and the zone with automatic fire alarm and firefighting measures, as is shown in Fig. 5.

Figure 5.

The fire risk zones in the original Gustav method

The Gustav method has a series of value principles for risk parameters. The evaluator could calculate the values of two axis and determine the position of fire risk in the rectangular coordinate system. The Gustav method provides owners with feasible and reasonable fire protection strategies according to the fire risk level located in the planar.

Scholars modified the original Gustav method into different versions for various assessed subjects, comparisons among modifications listed in Tables 3 and 4.

Table 3.

The modifications of Gustav method

Version	Origin [32]	Modified parameters [28]		Modified algorithm [29]
Empirical formulas	$GR=\frac{(Q_m·\alpha +Q_i)SL}{W{R}_i}$	$G{R}_s=\frac{(Q_m·\alpha +Q_i)SE}{W{R}_i(C_f+C_b)}$	Considered risk of large-scale processing equipment	$G{R}_t=\frac{(Q_m·\alpha +Q_i)S{R}_d}{W}$	Considered parameters of fire spread
			Separated firefighting competency into two aspects, firefighters and fire protection systems		Extracted firefighting competency
	$IR=kHDF$	$I{R}_s=k{H}_s{D}_s{F}_s$	Changed the value principles of parameters through establishing an index system with parameter weights	$IR=kHF\beta$	Deleted hazards to properties
					Added the number of people to consider hazards to life
	None	None	None	$C={\sum }_i{Z}_i{L}_i{\tau }_i\gamma +D_t$	Defined a new risk evaluation aspect, ‘Competency of fire-controlling’
Risk value	The Risk Profile	The Risk Profile	No change	The Risk Profile	Deleted transition region
	Visualization risk value in a rectangular coordinate system	Visualization risk value in a rectangular coordinate system	No change	Comprehensive Risk Value	$R=f(GR,IR,C)=\frac{\eta GR+\mu IR}{C}$
Application	All contributions	E-commerce Logistics Warehouses		Shopping Mall

Table 4.

The Meaning of Variables in Formulas

Variable	Meaning	Variable	Meaning	Variable	Meaning
$Q_m$	Mobile fire loads	$R_i$	Parameters of decreasing fire risk	$C_f$	Firefighting competency parameter of fire brigade
$Q_i$	Stationary fire loads	$k$	The feature parameter of people	$C_b$	Firefighting competency parameter of fire protection system
$\alpha$	Flammable parameter of $Q_m$	$F$	The parameter of gas	$\beta$	The parameter of population
$S$	Square meters of the constructions	$H$	Hazard parameter of life	$Z_i$	The parameter of firefighting competency of a fire brigade
$L$	Parameter of firefighting competency	$D$	The destroy risk parameter of property	$L_i$	The distance parameter of firefighting
$W$	Fire resistance parameter	$E$	Hazard parameter of equipment	${\tau }_i$	The height parameter of the building
$R_d$	Parameters of decreasing fire risk	$D_t$	Fire-controlling competency parameter of the construction	$\gamma$	The effect parameter of outdoor firefighting systems

The existed modifications of the Gustav method exhibited some drawbacks. On one hand, all the modified versions of empirical formula included rescue parameters into GR but didn’t make fire rescue powers independent of fire risk resources, which couldn’t quantify the effect of the effort of firefighting. On the other hand, the outcome of Gustav’s method is too simple to describe the fluctuation of the relative fire risk levels.

We separated the firefighting effort by defining a new empirical formula, named Control ability of fire protection (CA). In this way, Gustav’s method can modify from 2 to 3 dimensions, as shown in Fig. 6. We established a spatial rectangular coordinate system, defining GR as X-axis, IR as Y-axis, and CA as Z-axis. CA contains the fire rescue parameters, including firefighting facilities inside or outside, fire brigades, fire safety management. Each axis will be illustrated in detail below.

Figure 6.

Spatial diagram of the 3D Gustav method

The Formula of GR

Compared to the original formula in Gustav’s method, the modified GR alternates L, the parameter of firefighting power, to P and T, to distinguish the special characteristics of fire risk between technic processes. The modified expression of GR is formula (1):

$$GR=\frac{(Q_m·\alpha +Q_i)·S·P·T}{W·R_i}$$ 1

$Q_m$, mobile fire loads; $Q_i$, stationary fire loads; $\alpha$, flammable parameter of $Q_m$; S, square meters of logistics warehouse; P, district parameter of fire loads; T, the characteristics of technic process; W, the fire resistance parameter; $R_i$, the parameters of decreasing fire risk.

$Q_m$ is the main dynamic parameter, depending on the transit period of a specific logistics warehouse, while $\alpha$ changes with its fluctuation. Gustav method uses the isothermal value of standard wood, $\omega$, to value $Q_m$. Normally, $\omega$ can be valued by formula (2) [39]:

$$\omega =\raisebox{1ex}{$q$}\!\left/ \!\raisebox{-1ex}{$186$}\right.\mathit{kg}\left./,\right)m2$$ 2

While $q$ is the density of fire loads. So, we need to make sure the value of $q$. And the density of fire loads can be calculated by formula (3) [39]:

$$q=\frac{\sum M_g·\mathrm{\Delta }H}{A_c}$$ 3

While $q$ is the density of fire loads, MJ/m2; $M_g$, the mass of each good, kg; $\mathrm{\Delta }H$, the available heating value of the good, MJ/kg; $A_c$, the occupied area of the good.

It should be emphasized that the fluctuation of the density of fire loads is affected by the transit period of the logistics warehouse. We considered the effect to classify the transit period into three kinds, less than 2 days (like ‘zero storage’ warehouses), between 2 and 7 days (like transmit warehouses), and more than 7 days (like traditional warehouses).

The Formula of IR

The modified expression of IR is formula (4) [38]:

$$IR=0.1F·(H·\phi )·D$$ 4

While F is the parameter of toxic gas; H, hazard parameter of life; $\phi$, the number of people; D, the destroyed risk parameter of property.

Compared to the original formula in Gustav’s method, the modified GR pays attention to the change of people’s amount in specific technic process of a logistics warehouse. To make a balance between the maximum value in different axis, the result is calculated value multiplied by 0.1.

The Formula of CA

Control ability of fire protection (CA) refers to the comprehensive competency from fire protection equipment, workers, and firefighters to fire risk control in either daily safety management or fire accident, the sum of these three kinds of sub-competency. The expression of CA is formula (5):

$$CA=\sum _{i=1}^k{X}_i·L_i·H_i·E+I+Pi=1,2,3,...,k$$ 5

Each ingredient represents the extinguishing capacity respectively comes from firefighters, fire protection equipment indoor ($I$), and early fire extinguishing behaviors of workers $(P)$ in order. In the first ingredient, $X_i$ represents the firefighting capacity parameter of the fire brigade, $L_i$ represents the distance parameter of arriving fire accident site, $H_i$ represents the height parameter of logistics warehouse, and E represents the extinguish capacity parameter of fire equipment outdoor. And $k$ is the number of available fire brigader.

For $L_i$, the fire scale positively correlates with the distance between fire site and fire brigade when the arriving speed is stationary. According to Gustav’s method, $L_i$ is calculated by formula (6):

$$L_i=1-\frac{9d^2}{4v^2}(0<d\le \frac{2}{3}v)$$ 6

While d is the driving distance, m; $v$ is the driving speed, m/s.

Gustav considered the effect of the logistics warehouse height to fire rescue. And the height of the building won’t affect the fire rescue if the elevating high of a fire engine is taller than the building, vis versa. For $H_i$, it remains the original empirical formula in Gustav’s method but improves the available elevating high of the fire engine considering the technical development of the fire engine. $H_i$ can be calculated by formula (7) [33]:

$$H=\left\{\begin{array}{cc}1& (h_b\le h_f)\\ e^{[-0.023(h_b-h_f)]}& (h_b>h_f,h_f\gg 24)\end{array}\right)$$ 7

While $h_b$ is the building height, m; $h_f$ is the elevating high of the fire engine, m.

Based on the principle of the parameter values in Gustav method [39], we referenced the empirical value from renowned fire safety experts to discuss the values to each parameter, listed in Appendix 2. In this way, we can calculate both values of axis.

The Classification of Fire Risk Levels

Points in the spatial rectangular coordinates system are defined as the fire risk values. However, no user wants to gain a pile of figures, which doesn’t make sense, and even experts couldn’t judge straightly whether the fire risk is serious using these figures.

In extreme scenarios, the maximum of each axis can be calculated by specifying the best or worst conditions. We use cubes to classify the fire risk level, similar to how the original Gustav method distinguished fire risk levels. The X-axis, like the Y-axis, is divided into three intervals, while the Z-axis is divided into two intervals. As a result, the spatial rectangular coordinated system is made up of 18 cubes. And, in accordance with the international classification principle, these 18 cubes were classified into five risk levels. The 5-level evaluation set of fire risk levels is represented by the formula (8):

$$V=(V1,V2,V3,V4,V5)$$ 8

While the fire risk level grows up with the increase of the number.

The original Gustav method provides managers with reasonable fire protection measurements by dividing the axis into three areas, safety, transition, and danger. And the X-axis and Y-axis in modification also follow this separating way. But for Z-axis, it is different. On the one hand, the emergency capacity is changeable every day because many parameters depend on human behaviors. It is enough to judge the relativity of CA. On the other hand, it makes no sense to divide too many cubes, classified into five levels in the end.

For GR and IR, each parameter is classified into three levels, safety, transition, and danger. Then the results are naturally divided into three intervals. The interval nodes of GR are 0.62 and 6.89, while those of IR are 0.58 and 3.83. For CA, 9.3, the half of the maximum, is the interval node. The corresponding relations between 18 cubes and 5 fire risk levels are shown in Fig. 7.

Figure 7.

The spatial schematic diagram of fire risk level contribution. (a) The vertical view of fire risk level when CA > 9.3. There are five fire risk level, consistent with the upper part in (c). (b) The vertical view of fire risk level when CA < 9.3. There are four fire risk level, consistent with the down part in (c). (c) The front view of the 3D-Dynamic fire risk evaluation model

Compared with GR and IR, CA has the opposite mechanism of fire risk expression. The fire risk increases when the value of GR and IR goes up, while the higher value of CA illustrates maximum safety. The meaning of each fire risk level lists in Table 5.

Table 5.

The 5-Level Evaluation Set of Fire Risk Levels in Logistics Warehouse

Fire risk level	Meaning
V1	Scenario A. The warehouse, property, and people all have less exposure to fire risks, and the fire-controlling competency of construction is strong
V2	Scenario B. With the high fire-controlling competency, hazards to the logistics warehouse, or hazards to people and property are small
	Scenario C. The warehouse, property, and people have less exposure to fire risks although the fire-controlling competency of construction is weak
V3	Scenario D. With the high fire-controlling competency, hazards to the warehouse, property, and people are middle
	Scenario E. Although the fire-controlling competency of construction is weak, hazards to the warehouse, property, and people are below the average level
V4	Scenario F. The fire-controlling competency of construction is strong, but either hazards to the warehouse or hazards to property and people are bigger than the average level
	Scenario G. Although hazards to the warehouse, property, and people are below the average level, the fire-controlling competency of construction is weak
V5	Scenario H. The warehouse, property, and people all have more exposure to fire risks, while the fire-controlling competency of construction is strong
	Scenario I. Only if hazards to the warehouse, or hazards to property and people is big, adding the weak fire-controlling competency of the logistics warehouse

Application Instruction

Combining the above researches, we develop a 3D-Dynamic fire risk assessment method of logistics warehouses. The instruction can conclude into ‘5C’, Collection, Calculation, Curve tracing, Classification, and Correction in order.

Collect data of the assessed logistics warehouse. Users can gain fixable data through investigating the status quo of the assessed subject, including construction quo (area, layer), operation quo (function, goods category, transit period), fire protection quo (fire resistance class, firefighting equipment, fire load), and other aspects listed in the index system. For dynamic data, users need to record the values of dynamic risk parameters during more than one transit period without maximum limitation.

Calculate the values of risk parameters in empirical formulas. Determining the value of each risk parameter according to the collected data, users put values into the empirical formulas of the 3D Gustav’s method and gain the outcome of three axes.

Tracing the curve into the spatial rectangular coordinate system. A series of spatial points, describing GR, IR, and CA, can be drawn in the spatial rectangular coordinate system, while the curve reveals the temporal fluctuation of the fire risk.

There are five steps to model them.

Firstly, the user should collect data from the assessed logistics warehouse. Basic data, such as construction area, layers, operation function, goods category, etc., corresponding to $A_1$ in the index system, are easy to collect. For fire protection factors, such as fire protection design, fire safety management, and fire emergency strategy, corresponding to $A_2,A_3,A_4$ in the index system, users need to check one by one, and gain the score of each parameter. For example, if the automatic sprinkler system in the assessed logistics warehouse is available and in perfect condition, the value of the automatic sprinkler system, one of the parameters of I, is 100 according to Table 24. And for dynamic parameters, such as fire loads, populations, transit period, etc., users need to record the values of dynamic risk parameters during more than one transit period without maximum limitation.

Table 24.

The Value Principle of I

Fire protection measures	Values in different levels
	10	40	60	100
Automatic fire alarm system1	None	Regional control	Centralized control	Controller control
Fire power supply	Not qualified	Partially qualified	Mostly qualified	Qualified2
Electrical fire protection	Poor	Qualified	Good	Excellent
Fire hydrant system indoor	Not qualified	Partially qualified	Mostly qualified	Qualified
Automatic sprinkler system	Not qualified	Partially qualified	Mostly qualified	Qualified
Smoke control system	Not qualified	Partially qualified	Mostly qualified	Qualified
Fire curtain at firewall	Breakdown	–	–	Normal
Fire curtain near conveyor belts	Breakdown	–	–	Normal
Fire compartment	Not qualified	–	–	Qualified

1. There are three types of automatic fire alarm system in Fire Code, respectively suiting to different building levels.

2. ‘Qualified’ means that the measure reaches the standard of the relevant codes.

Secondly, the collected value of each parameter multiplies the corresponding weight in the index system (Table 8 in Appendix 1), and the results are the value of parameters in empirical formulas. For example, if each fire protection factor of $I$ scores 100, then the value of I will be:

$$I=100·\left(C_{20},+,C_{21},+,C_{22},+,C_{23},+,C_{24},{+C}_{25},+,C_{27},+,C_{28},+,C_{29}\right)=100\left(0.0333,+,0.0109,+,0.0167,+,0.0029,+,0.0069,+,0.0044,+,0.0092,+,0.0057,+,0.0203\right)=11.03$$

Table 8.

The Weights of Fire Risk Parameters in Index System

First level index		Second level index		Third level index		Comprehensive weight
Parameter	Weight	Parameter	Weight	Parameter	Weight
A1	0.5349	B1	0.8333	C10	0.2000	0.0892
				C11	0.8000	0.3566
		B2	0.1667	C12	0.5414	0.0483
				C13	0.2313	0.0206
				C14	0.0751	0.0067
				C15	0.1522	0.0136
A2	0.1504	B3	0.5000	C20	0.4434	0.0333
				C21	0.1443	0.0109
				C22	0.2223	0.0167
				C23	0.0391	0.0029
				C24	0.0919	0.0069
				C25	0.589	0.0044
		B4	0.5000	C26	0.5318	0.0400
				C27	0.1221	0.0092
				C28	0.0760	0.0057
				C29	0.2702	0.0203
A3	0.2456	B5	0.75000	C30	0.4723	0.0870
				C31	0.2854	0.0526
				C32	0.1697	0.0313
				C33	0.0725	0.0134
		B6	0.25000	C34	0.2500	0.0154
				C35	0.7500	0.0461
A4	0.0691	B7	0.0837	C40	0.6667	0.0039
				C41	0.3333	0.0019
		B8	0.5450	C42	0.6483	0.0244
				C43	0.1220	0.0046
				C44	0.2297	0.0086
		B9	0.1385	C45	0.3333	0.0032
				C46	0.6667	0.0064
		B10	0.2329	C47	0.2297	0.0037
				C48	0.6483	0.0104
				C49	0.1220	0.0020

Thirdly, determining the value of each risk parameter according to the collected data, users put values into the empirical formulas of the 3D Gustav’s method and gain the outcome of three axes.

Fourthly, tracing the curve into the spatial rectangular coordinate system. A series of spatial points, describing GR, IR, and CA, can be drawn in the spatial rectangular coordinate system, while the curve reveals the temporal fluctuation of the fire risk.

Lastly, users can evaluate the fire risk level of the assessed logistics warehouse according to the 3D graph. The spatial rectangular coordinated system is made up of 18 cubes, while the X-axis and the Y-axis are both divided into three intervals while the Z-axis is divided into two intervals. And following the international classification principle, these 18 cubes were classified into five risk levels, as shown in Fig. 7. For classifying the fire risk level, the curve by which the cube penetrate through is what the fire risk level is at one specific period. It is clear to summarize the fluctuation of fire risk level.

Correct dangerous parameters and decrease the fire risk level. Users can distinguish periods with the high-risk level and analyze why they are so high. Then they can take reasonable mitigation to correct the state quo of hazards and decline the fire risk. In this way, safety managers needn’t treat all warehouses without discrimination but pays more attention to dangerous buildings in specific periods. And the efficiency of management will naturally improve.

Furthermore, the modified version still inherits the original intention of Gustav’s method, which is to provide users with a feasible suggestion to improve safety level instead of quantum of changeable numbers.

Case Study

The manager of Jingdong Gu’an logistics park provided us with two logistics warehouses, a sorting center warehouse, and a transit warehouse in the second construction of the logistics park, to do an empirical study. This logistics park had a fire accident in 2016, causing more than 1 billion in insurance compensation, which woke the fire safety consciousness.

The layout of the logistics park is shown in Fig. 8. The sorting center warehouse is NO. 5, and the transit warehouse is NO. 7. Two warehouses are not independent, while NO. 7 selects goods according to the orders and transit to NO. 5 to pack and transport to the destination. And we follow the ‘5C’ procedures to assess the fire risks of these warehouses.

Figure 8.

The basic situation of the empirical subjects

All constructions in Jingdong Gu’an logistics park should be designed according to the relevant fire safe regulations. For negative fire protection measures, each warehouse was designed with proper fire compartmentations, fire resistances according to Code for fire protection design of buildings (GB 50,016–2014). For positive fire protection measures, each warehouse installed fire hydrant system indoor and outdoor, sprinkler system, automatic fire alarm system, according to the Technical code for fire protection water supply and hydrant systems (GB 50,974–2014), the Code for design of sprinkler system (GB 50,084–2017), the Code for design of automatic fire alarm system (GB 50,116–2013). And the logistics park satisfied the fire safety requirements in the General rules for fire safety management of storage occupancies (GA 1131–2014).

Both NO. 5 and 7 installed automatic fire protection systems, including fire hydrant system indoor and outdoor, sprinkler system, automatic fire alarm system, fire water tank etc.

Fire Risk Evaluation of Sorting Center Warehouse (NO. 5)

NO. 5 is 20762.28 m² with three fire compartments, and it is used to pack, sort, and distribute goods. Automatic sorting equipment, the conveyor belts of which lay across each other, occupies almost all areas.

The categories and amount of goods in NO. 5 depends on the orders. Besides the goods from NO. 7, the goods also come from other warehouses or trucks to make accurate prediction impossible. Generally, most of the goods include small electrical appliances, office supplies, mobile phones or computers, followed by daily necessities and wine.

Field investigation revealed the current state of fire risk, as shown in Fig. 9. The goods in the sorting area were disorganized due to insufficient sorting. Goods or cartons were used to cover the fire engine road outside and the fire hydrants inside. The security guards at the entrance were strict about who came in and out, but there were no monitors in the loading and unloading area, where people could come and go as they pleased.

Figure 9.

The fire safety status quo of NO. 5. (a) The goods in the sorting area were disordered (left picture), even the cotton goods were above the lubricating oil. (b) The fire engine road outdoor and the fire hydrants indoor were covered by goods or cartons (right picture)

NO.5 operates from 7 to 2 am the next day and should have zero mobile fire loads when it closes. We chose the worktime to record the data of dynamic parameters. The mobile fire loads were recorded each half-hour during the work time. There are 135 workers on average and up to 200 in shopping festivals, while half of the workers rest at lunch or dinner. The parameters of NO.5 are listed in Table 6. The curve tracing is shown in Fig. 10.

Table 6.

Values of Fire Risk Parameters in Sorting Center Warehouse (NO. 5)

Factor	Value	Factor	Value	Factor	Value	Factor	Value	Factor	Value	Factor	Value
α	1.6	B	1.4	T	0.0206	D	3	Li	1	I	7.127
Qi	0	W	1.6	F	1.2	φ	3or2	hi	1	P	6.73
S	4	Ri	1.3	H	1.5	Xi	4.192	E	0.741	–	–

Figure 10.

The curve tracing of fire risk value in NO. 5

The fire risk curve showed that NO. 5 stays at V2, the safe state, from 7 to 8:30 am and after 1 am, while other operating time is at V3, the middle fire risk level. Above all, the sorting center warehouse (NO. 5) is relatively safe though the mobile loads go up and down every moment. That is because of the strict requirement of zero fire load when there are no workers.

Fire Risk Evaluation of Transmit Warehouse (NO.7)

NO. 7 is just 200 m² bigger than NO. 5 but with six fire compartments because of its storage function. It composes high-layer shelves and general shelves. The conveyor belts were around the warehouse to conveniently transit goods to NO. 5. The firewalls between the two warehouses were crossed by conveyor belts many times so that the owner could install many fire-roller shutters at the holes.

Field investigation disclosed fire risk state quo, as is shown in Fig. 11. According to the building codes, NO. 7 belongs to Class C in the warehouse category, limited to storing flammable goods. However, we found aerosols deposited with yoga mats. And some goods were deposited below the conveyor belts, even some below the fire roller shutters.

Figure 11.

The fire safety status quo of NO. 7. (a) The goods below the conveyor belts (left picture). When the goods ignite, the fire will spread to another warehouse from the holes in the firewall. (b) The goods below the fire roller shutter (right picture). It makes the fire roller shutter no sense because the goods hinder the operation of the fire roller shutter

NO. 7 transits goods about 2 to 3 days, depending on the orders. We recorded the fire loads by retrieving order documents for the past 2 weeks. NO. 7 operates all day and needs 45 workers in the daytime (7 am to 5 pm), 25 workers at night (5 pm to 7 am the next day). The parameters of NO. 7 are listed in Table 7. The curve tracing is shown in Fig. 12.

Table 7.

Values of Fire Risk Parameters in Transmit Warehouse (NO. 7)

Factor	Value	Factor	Value	Factor	Value	Factor	Value	Factor	Value	Factor	Value
α	2.0	B	1.8	T	0.0136	D	1/3/4	Li	1	I	7.127
Qi	0	W	2	F	1.5	φ	1	hi	1	P	6.73
S	4	Ri	1.0	H	1.2	Xi	4.192	E	0.741	–	–

Figure 12.

The curve tracing of fire risk value in NO. 7

The fire risk curve showed that the transit warehouse (NO. 7) contains V2 or a higher fire risk level. However, the fluctuation of the fire risk is significant. From the top view, the fire risk level of NO. 7 revolves around V2 to V3, which should be contributed to fire protection equipment and mitigations because the CA stayed at the ‘good’ interval.

Results and Discussion

Analysis of the Evaluation Results

Comparing the fire risk level interval, two modern logistics warehouses seemed equal. However, if we compare the amplitudes of fire risk fluctuation, we may find that the fire risk fluctuation in NO. 5 is larger than that in NO. 7. The fire risk in NO. 5 is significantly affected by GR, while GR and IR contribute to the fire risk level in NO. 7 together. And we also noticed that the fire risk level in NO. 7 intensively stays at the higher level. And more specific-context factors should be considered. For example, the working time of NO. 7 is 24 h while NO. 5 just opens 18 h, and there should be zero mobile fire loads when workers in NO. 5 work off. Above all, the fire risk level of NO. 7 may be higher than that of NO. 5, although the time unit of record in the two logistics warehouses is different.

Practical Application

The research goal doesn’t just calculate the fire risk level or the amplitude of fire risk fluctuation but describes how fire risk changes and improves the vigilance when fire risk increases. This method suits to fire risk evaluation of modern logistics warehouses, especially storing warehouses, sorting center warehouses, and transit warehouses. With the increasing demands of logistics, advanced technologies, and transportation capacity, new logistics warehouses type will be developed, such as the automatic modernized logistics warehouses with a clearance height of over 14 m. This fire risk evaluation method needs to be improved following the development of the logistics industry to cover as many risk factors as possible.

For different kind of logistics warehouses, there are various mitigation measures. For example, the evaluation result of NO. 7 shows that the fire risk level will increase when most of the goods stay in storing phase. At that time, safety managers should limit the input amount of goods to control the fire risk level at the safe interval or increase patrol intensity with higher vigilance.

This new fire risk evaluation method of modern logistics warehouses is superior in five aspects by comparing with other existing methods. Compared with the Safety Checklist method (SCL) listing some rough risk exposures for managers to check, this 3D-Dynamic Gustav method evaluates fire risk more accurately. Compared with the general AHP method, this 3D-Dynamic Gustav method uses a new index system of fire risk evaluation for modern logistics warehouses, considering the risk of various process characteristics (B2), the risk of different fire shutters (C27, C28), garbage materials (C32), and adjusting traditional weight of the evacuation factors. Compared with the original Gustav method, this 3D-Dynamic Gustav method can assess fire risk dynamically in three-dimensional view. Users input changeable values of each fire risk parameter in real-time and this method outputs dynamic fluctuation of fire risk level time-dependently. Compared with the fuzzy analytical method, this 3D-Dynamic Gustav method is more practical for grassroots safety managers. Compared with other methods, this 3D-Dynamic Gustav method is popular. We invited fire safety managers working at JingDong Logistics Park to experience this 3D-Dynamic Gustav method. Users’ feedback improved that the new method is feasible and practical even for laypeople with little professional knowledge because of its spatial view and concise procedures.

Conclusion

The study creates a 3D-Dynamic fire risk evaluation method for logistics warehouse grassroots safety managers based on the Gustav method.

Following a review of fire accidents and fire protection research, the majority of existing fire risk evaluation methods for logistics warehouses result in a stationary fire risk value for a specific warehouse. Among the various fire risk evaluation methods, the Gustav method meets the needs of the end-users. However, neither the original Gustav method nor its modifications place a premium on emergency fire control, which may result in unnecessary economic costs.

Considering the drawbacks of previous studies, we extracted parameters correlating fire protection to define the control ability of fire protection as CA, also defined as the Z-axis at the same time. In this way, the planar rectangular coordinate system established by the Gustav method extends to the spatial one. The parameters in empirical formulas are composed of stationary ones and dynamic ones. Each parameter determines by multiplying experienced value and weight, the former component obeys the value principles in the Gustav method while the latter one is determined by the fire risk evaluation index system of logistics warehouses. Fire protection factors are scored according to the value principle tables and field investigation, and calculated final value through using score multiplies the weight in the fire risk index system. The spatial points defined as fire risk values are separated into 18 cubes classifying five fire risk levels.

The empirical study above identified the novel method as a necessary tool for fire risk evaluation of logistics warehouse, but there are still limitations. The recording period in the empirical study is at a singular time. The interviewed workers reflected that the management was disordered when the shopping festivals came, marking the peak value of fire risk. Moreover, the government supervising officers suggested that the end-users of the assessment method shouldn’t only include safety managers. When the mitigations of fire risks conflict the benefits of the company, safety managers may ignore the fire risk. If supervising officers record the fluctuation of fire risk at the same frequency, cheating behaviors will be reduced to minimum.

And the quantitative evaluation is challenging. Big data technology can make up for the lack of data. IoT is prevalent in transmitting subject-to-subject information. With the support of logistics IoT platforms, the weights and values of risk parameters in empirical formulas can be calculated quantitatively. Meanwhile, insurance for logistics warehouse fire accidents combing fire risk evaluation is also a significant research direction.

Appendix 1 The weights of fire risk parameters in index system

Combined Delphi Method and Analytic hierarchy process (AHP) method, the weights of parameters could be calculated, as is shown in Table 8. And the result of consistency test of judgement matrix is well.

See Table 8.

Appendix 2 The value principles of fire risk parameters

See Tables 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.

Table 9.

The Value Correlations Between Q_m and ω and

$\omega$, kg/m2	0–100	101–200	201–500	501–1000	1001–1600	≥ 1601
Q m	0–10	11–20	21–30	31–40	41–50	60

Table 10.

The Value Correlations Between Combustibles’ Category and α

Combustibles’ category	$\alpha$
Food and agricultural products	0.8
Decoration materials (including wooden beams and columns, ceiling, floor, etc.)	1.0
Fiberboard, cotton-free products, polyester mattresses	1.2
Plastic products (including household appliances, office supplies)	1.4
Daily textiles (including yoga mat, cotton towel, hemp products, chemical fiber, etc.)	1.6
Cotton crops (raw or seed cotton) and food crops	1.8
Chemicals (including daily chemical products, oil, aerosols, etc.)	2.0

Table 11.

Judgement Rule of Multiple Categories of Combustibles [34]

The proportion of combustible category with higher-risk level	Judgement rule
< 10%	The combustible category depends on which mass proportion is over 90%
10–25%	The combustible category depends on which mass proportion is over 75%
> 25–50%	The combustible category depends on the higher-risk-level combustible which mass proportion is over 25%

Table 12.

The Value Principle of Q_i

Density of the combustible (kg/m2)	Material of the structural support	Material of the ceiling	Material of the wall	$Q_i$
0–20	Concrete, brick, or steel	Concrete or steel	Concrete, brick, or steel	0
21–45	Steel	Wood	Concrete or steel	2
46–70	Wood or steel	Wood	Concrete or brick	4
71–100	Wood	Wood	Tile, wood, or iron	6

Table 13.

The Value Principle of S

Construction area, m2	$S$	Construction area, m2	$S$	Construction area, m2	$S$
4000–8000	0–1	20,001–24,000	4–5	36,001–40,000	8–9
8001–12,000	1–2	24,001–28,000	5–6	> 40,000	9–10
12,001–16,000	2–3	28,001–32,000	6–7	–	–
16,001–20,000	3–4	32,001–36,000	7–8	–	–

Table 14.

The Value Principle of B

Level	Ignition area				$B$
	Occupation	Height	Layer	Fire compartment
1	Office area	< 8 m	Single layer	< 1500 m2	1.0
2	Loading and unloading area	8–14 m	Single layer	1500–2000 m2	1.2
3	Sorting center	8–14 m	Multiple layer	2000–2500 m2	1.4
4	Manufacturing area	> 14 m	Multiple layer	2500–3500 m2	1.6
5	Storing area	> 14 m	Multiple layer	> 3500 m2	1.8
6	Elevated warehouse	> 20 m	Multiple layer	> 3500 m2	2.0

Table 15.

The Value Principle of T

Process characteristics	Thermoplastic and manufacturing	Sorting and packing	Loading and transportation	storing
T	0.0483	0.0206	0.0067	0.0136

Table 16.

The Value Principle of W

Fire resistance level	First level	Second level	Third level
W	2	1.6	1.2

Table 17.

The Value Principle of R_i

Num	State	$R_i$
1	There are large fire loads with the inflammable, large-scale area per layer, delayed waste cleaning, causing fire to spread quickly	1.0
2	There are large fire loads with the combustible, or no consciousness of goods classification, causing fire to spread quickly	1.3
3	There are fire-retardant goods with good ventilation and strict safety management	1.6
4	There are fire-retardant or non-combustible goods with reasonable fire compartments, defending fire to spread	2.0

Table 18.

The Value Principle of F

Num	The toxicity of combustibles	$F$
1	Timber, grain, cotton, paper, etc	1.0
2	Daily necessities (yoga mat, clothing, chemical fiber fabric)	1.2
3	Oil, aerosols, daily chemicals, etc	1.5
4	Household appliances, synthetic plastics, etc	1.7
5	Steel structure fire retardant coating, rubber, etc	2.0

Table 19.

The Value Principle of H

Num	The status quo of evacuation system	H
1	When the fire broadcasting, emergency lights, and indication signs work well, the evacuation pathway is unblocked	1.0
2	When the indicating broadcasting and the emergency lights work well, the evacuation pathway is unblocked	1.2
3	When just alarm bells ringing without any signs, the evacuation pathway is not safe	1.5
4	When there is no fire broadcasting, emergency lights, or indication signs, the evacuation pathway is blocked	2.0

Table 20.

The Value Principle of D

Risk level	Danger level	D
1	The logistics warehouse without large-scale process equipment is in-transit period, and the capacity of goods is low	1
2	The logistics warehouse without large-scale process equipment contains fewer valuable goods	2
3	The logistics warehouse with large-scale process equipment includes sorting center or manufacturing function	3
4	The logistics warehouse with large-scale process equipment attains the capacity peak of goods	4

Table 21.

The Value Principle of φ

Population	$\phi$	Population	$\phi$	Population	$\phi$
0–50	1	151–200	4	301–350	7
51–100	2	201–250	5	351–400	8
101–150	3	251–300	6	–	–

Table 22.

The Value Principle of X_i

Parameter	Value of different levels
	10	40	60	100
Fire brigade corresponding time	> 20 min	15–20 min	10–15 min	< 10 min
Number of firefighters	Serious lack	Insufficient	Enough	Sufficient
Quantity and quality of firefighting equipment	Poor	Qualified	Good	Excellent
Fire emergency plan	No	Simple	Normal	Comprehensive
Field operation plan	No	Unreasonable	Reasonable	Practical

Table 23.

The Value Principle of E

Parameters	Values in different levels
	10	40	60	100
Fire rescue road	Blocked/Occupied	–	Partially passable	Qualified
Fire hydrant system outdoor	Useless	Partially useful	Qualified	–
Water source for fire rescue	None	Qualified	Sufficient	–

Table 25.

The Value Principle of P

Parameters	Values in different levels
	10	40	60	100
Fire safety propaganda	None	Poor	Qualified	Excellent
Fire rescue drill	None	Poor	Qualified	Excellent
Firefighting training	None	Poor	Qualified	Excellent
Fire safety knowledge & skills	None	Poor	Qualified	Excellent

Appendix 3 The numerical results of the empirical study

See Tables 26, 27, 28, 29

Table 26.

The Real-Time Value of Q_m in NO. 5

Time	$q$	$Q_m$	Time	$q$	$Q_m$	Time	$q$	$Q_m$
7:00	0.0	0	14:00	9437.5	31	21:00	13,495.7	35
7:30	346.7	2	14:30	6734.1	26	21:30	17,834.3	38
8:00	683.5	4	15:00	8536.9	27	22:00	20,534.5	42
8:30	992.9	6	15:30	12,438.4	34	22:30	13,679.3	35
9:00	2591.4	14	16:00	15,289.7	36	23:00	9895.2	32
9:30	3478.1	17	16:30	19,478.8	42	23:30	4523.7	21
10:00	4850.3	22	17:00	24,489.5	45	00:00	2476.8	13
10:30	6940.2	26	17:30	26,894.5	47	00:30	1464.0	8
11:00	8980.4	29	18:00	30,100.5	60	01:00	1034.2	6
11:30	12,580.6	34	18:30	32,205.6	60	01:30	475.6	3
12:00	19,479.2	41	19:00	33,498.1	60	02:00	0.0	0
12:30	24,340.0	45	19:30	25,734.6	45	02:30	0.0	0
13:00	29,840.5	60	20:00	17,783.3	38	03:00	0.0	0
13:30	18,730.6	40	20:30	10,038.9	32	03:00	0.0	0

Table 27.

The Numerical Results of Three Axis in NO. 5

Time	GR	IR	CA	Time	GR	IR	CA	Time	GR	IR	CA
7:00	0	0	16.96	14:00	2.75	1.08	16.96	21:00	3.11	2.16	16.96
7:30	0.18	2.16	16.96	14:30	2.31	2.16	16.96	21:30	3.37	2.16	16.96
8:00	0.35	2.16	16.96	15:00	2.40	2.16	16.96	22:00	3.73	2.16	16.96
8:30	0.53	2.16	16.96	15:30	3.02	2.16	16.96	22:30	3.11	2.16	16.96
9:00	1.24	2.16	16.96	16:00	3.19	2.16	16.96	23:00	2.84	2.16	16.96
9:30	1.51	2.16	16.96	16:30	3.73	2.16	16.96	23:30	1.86	2.16	16.96
10:00	1.95	2.16	16.96	17:00	3.99	2.16	16.96	00:00	1.15	2.16	16.96
10:30	2.31	2.16	16.96	17:30	4.17	2.16	16.96	00:30	0.71	2.16	16.96
11:00	2.57	2.16	16.96	18:00	5.32	1.08	16.96	01:00	0.53	2.16	16.96
11:30	3.02	2.16	16.96	18:30	5.32	1.08	16.96	01:30	0.27	2.16	16.96
12:00	3.64	1.08	16.96	19:00	5.32	1.08	16.96	02:00	0	0	16.96
12:30	3.99	1.08	16.96	19:30	3.99	1.08	16.96	02:30	0	0	16.96
13:00	5.32	1.08	16.96	20:00	3.37	1.08	16.96	03:00	0	0	16.96
13:30	3.55	1.08	16.96	20:30	2.84	2.16	16.96	03:00	0	0	16.96

Table 28.

The Real-Time Value of Q_m in NO. 7

Time	$q$	$Q_m$	Time	$q$	$Q_m$	Time	$q$	$Q_m$
1.1	28,693.8	49	1.6	34,902.7	60	1.11	14,352.2	35
1.2	34,982.5	60	1.7	15,843.8	36	1.12	10,354.4	32
1.3	35,499.1	60	1.8	28,098.9	49	1.13	25,303.8	46
1.4	11,909.4	33	1.9	34,975.4	60	1.14	26,305.5	47
1.5	29,674.5	50	1.10	33,424.3	60	1.15	32,339.1	60

Table 29.

The Numerical Results of Three Axis in NO. 7

Time	GR	IR	CA	Time	GR	IR	CA	Time	GR	IR	CA
1.1	4.80	0.36	16.96	1.6	6.92	1.44	16.96	1.11	3.43	0.18	16.96
1.2	6.92	1.44	16.96	1.7	3.53	0.18	16.96	1.12	3.13	0.18	16.96
1.3	6.92	1.44	16.96	1.8	4.80	0.36	16.96	1.13	4.50	0.36	16.96
1.4	3.23	0.18	16.96	1.9	6.92	1.44	16.96	1.14	4.60	0.36	16.96
1.5	4.90	0.36	16.96	1.10	6.92	1.44	16.96	1.15	6.92	1.44	16.96

Declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.