Featured risk evaluation of nautical navigational environment using a risk cloud model

Figures & data

Figure 1. The normal cloud model $C(22,3,0.2)$ indicating ‘Youth’.

Figure 2. Cloud generators (left: the forward cloud generator; right: the backward cloud generator).

Table 1. Relationship between linguistic and numerical variables.

Type	Name	Symbol	Domain of discourse
Linguistic	Risk comment	rcmt	From L to H, and holding five benchmark values: L, ML, M, MH, H
Numerical	Risk degree	$D^{\mathrm{R}}$	$\text{[}\begin{array}{cc}{D}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{R}}& D_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{R}}]\end{array}=[\begin{array}{cc}0& 1]\end{array}$

Table 2. The golden section based algorithm for calculating the parameters of five benchmark RCMs.

		Cloud model (Characteristic parameters)
Sequence number ($k$)	Cloud model symbol	$Ex$	$En$	$He$
−2	$C_{-2}$	$D_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{R}}$	$E{n}_{-1}/0.618$	$H{e}_{-1}/0.618$
−1	$C_{-1}$	$E{x}_0-0.382\times {\displaystyle \frac{(D_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{R}}+D_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{R}})}{2}}$	$0.382\times {\displaystyle \frac{D_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{R}}-D_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{R}}}{6}}$	$H{e}_0/0.618$
0	$C_0$	${\displaystyle \frac{D_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{R}}+D_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{R}}}{2}}$	$0.618\times E{n}_{+1}$	designated $H{e}_0$
+1	$C_{+1}$	$E{x}_0+0.382\times {\displaystyle \frac{(D_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{R}}+D_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{R}})}{2}}$	$0.382\times {\displaystyle \frac{D_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{R}}-D_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{R}}}{6}}$	$H{e}_0/0.618$
+2	$C_{+2}$	$D_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{R}}$	$E{n}_{+1}/0.618$	$H{e}_{+1}/0.618$

Figure 3. Reference scale: appearances of benchmark RCMs corresponding to the five linguistic terms.

Table 3. Reference scale: parameters of benchmark RCMs corresponding to the five linguistic terms.

				Cloud model (characteristic parameters)
Sequence number ($k$)	Linguistic term	Typical value (=$Ex$)	Cloud model symbol	$Ex$	$En$	$He$
−2	L	0	$C_{\mathrm{L}}$ ($=C_{-2}$)	0	0.1031	0.013
−1	ML	0.309	$C_{\mathrm{M}\mathrm{L}}$ ($=C_{-1}$)	0.309	0.064	0.008
0	M	0.5	$C_{\mathrm{M}}$ ($=C_0$)	0.5	0.039	0.005
+1	MH	0.691	$C_{\mathrm{M}\mathrm{H}}$ ($=C_{+1}$)	0.691	0.064	0.008
+2	H	1	$C_{\mathrm{H}}$ ($=C_{+2}$)	1	0.1031	0.013

Table 4. An example questionnaire: the core part.

	Linguistic term
Initial evaluation	L	ML	M	MH	H
A concerned object

Figure 4. Step-wise approach to risk evaluation of NNEt by using the RCM.

Figure 5. The specific area of interest.

Table 5. System analysis and the concerned object.

Top layer	Middle layer	Bottom layer: constituent factor- concerned object
The NNEt of Hangzhou Bay Sea-crossing Bridge Waters	Natural environment	Wind
		Current
		Fog and visibility
	Channel condition	Channel width
		Channel water depth
		Shipping route cross
	Traffic environment	Ship traffic flow volume
		Obstacles to navigation
		Navigational aids

Table 6. The initial qualitative risk evaluation of the concerned objects by 20 experts.

		Linguistic term (for qualitative risk evaluation)
Initial qualitative risk evaluation		L	ML	M	MH	H
Concerned object	Wind	0	2	4	11	3
	Current	0	1	4	11	4
	Fog and visibility	1	1	8	8	2
	Channel width	3	5	10	2	0
	Channel water depth	1	2	10	6	1
	Shipping route cross	6	2	9	2	1
	Ship traffic flow volume	2	5	8	4	1
	Obstacles to navigation	4	4	4	7	1
	Navigational aids	4	7	6	3	0

Note: The value in the table represent the total number of experts who used the linguistic term to evaluate an object.

Table 7. Final RCM of the concerned object.

Concerned object	The RCM ($C^{\mathrm{R}}$)
Wind	$C^{\mathrm{R}}(0.6610,0.0649,0.0082)$
Current	$C^{\mathrm{R}}(0.6955,0.0688,0.0084)$
Fog and visibility	$C^{\mathrm{R}}(0.5919,0.0599,0.0076)$
Channel width	$C^{\mathrm{R}}(0.3964,0.0574,0.0073)$
Channel water depth	$C^{\mathrm{R}}(0.5382,0.0554,0.0070)$
Shipping route cross	$C^{\mathrm{R}}(0.3750,0.0664,0.0084)$
Ship traffic flow volume	$C^{\mathrm{R}}(0.4655,0.0599,0.0075)$
Obstacles to navigation	$C^{\mathrm{R}}(0.4356,0.0688,0.0087)$
Navigational aids	$C^{\mathrm{R}}(0.3618,0.0643,0.0081)$

Figure 6. RCM appearance of the object ‘Wind’.

Figure 7. RCM appearance of the object ‘Current’.

Figure 8. RCM appearance of the object ‘Fog and visibility’.

Figure 9. RCM appearance of the object ‘Channel width’.

Figure 10. RCM appearance of the object ‘Channel water depth’.

Figure 11. RCM appearance of the object ‘Shipping route cross’.

Figure 12. RCM appearance of the object ‘Ship traffic flow volume’.

Figure 13. RCM appearance of the object ‘Obstacles to navigation’.

Figure 14. RCM appearance of the object ‘Navigational aids’.

Table 8. Quantitative evaluation based on fuzzy theory.

Concerned object	Fuzzy theory-based risk degree ($D_{\mathrm{F}\mathrm{T}}^{\mathrm{R}}$)
Wind	0.6610
Current	0.6955
Fog and visibility	0.5919
Channel width	0.3964
Channel water depth	0.5382
Shipping route cross	0.3750
Ship traffic flow volume	0.4655
Obstacles to navigation	0.4356
Navigational aids	0.3618