Damage effectiveness assessment method for anti-ship missiles based on double hierarchy linguistic term sets and evidence theory

doi:10.23919/JSEE.2022.000041

Abstract

Abstract:

The research on the damage effectiveness assessment of anti-ship missiles involves system science and weapon science, and has essential strategic research significance. With comprehensive analysis of the specific process of the damage assessment process of anti-missile against ships, a synthetic damage effectiveness assessment process is proposed based on the double hierarchy linguistic term set and the evidence theory. In order to improve the accuracy of the expert’s assessment information, double hierarchy linguistic terms are used to describe the assessment opinions of experts. In order to avoid the loss of experts’ original information caused by information fusion rules, the evidence theory is used to fuse the assessment information of various experts on each case. Good stability of the assessment process can be reflected through sensitivity analysis, and the fluctuation of a certain parameter does not have an excessive influence on the assessment results. The assessment process is accurate enough to be reflected through comparative analysis and it has a good advantage in damage effectiveness assessment.

Key words: anti-ship missile, damage effect assessment, linguistic term set, evidence reasoning

Tianle YAO, Weili WANG, Run MIAO, Jun DONG, Xuefei YAN. Damage effectiveness assessment method for anti-ship missiles based on double hierarchy linguistic term sets and evidence theory[J]. Journal of Systems Engineering and Electronics, 2022, 33(2): 393-405.

Figures/Tables 19

Fig 1

Fig 2

Fig 3

Table 1

Assessment linguistic results assessed by four experts"

Criterion	Expert 1			Expert 2			Expert 3			Expert 4
Criterion	A₁	A₂	A₃	A₁	A₂	A₃	A₁	A₂	A₃	A₁	A₂	A₃
C₁₁	$ \left\{ {{S_{3\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $
C₁₂	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $
C₁₃	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $
C₁₄	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $
C₁₅	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 2\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $
C₁₆	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $
C₁₇	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $
C₁₈	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $
C₁₉	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $
C₂₁	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $
C₂₂	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $
C₂₃	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $
C₂₄	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $
C₂₅	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $
C₂₆	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $
C₂₇	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $

Table 1

Table 2

Table 3

Fig 4

Fig 7

Fig 5

Fig 6

Table 4

Table 5

Fig 8

Table 6

Fig 9

Table 7

Fig 11

Fig 10

Fig 12

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Criterion	Expert 1			Expert 2			Expert 3			Expert 4
Criterion	A₁	A₂	A₃	A₁	A₂	A₃	A₁	A₂	A₃	A₁	A₂	A₃
C₁₁	0.2494	0.2533	0.2494	0.2506	0.2497	0.2506	0.2506	0.2437	0.2506	0.2494	0.2533	0.2494
C₁₂	0.2503	0.2515	0.2524	0.2503	0.2515	0.2500	0.2491	0.2455	0.2452	0.2503	0.2515	0.2524
C₁₃	0.2494	0.2509	0.2494	0.2506	0.2485	0.2506	0.2506	0.2497	0.2506	0.2494	0.2509	0.2494
C₁₄	0.2497	0.2521	0.2521	0.2485	0.2521	0.2509	0.2521	0.2437	0.2449	0.2497	0.2521	0.2521
C₁₅	0.2509	0.2512	0.2518	0.2449	0.2537	0.2494	0.2533	0.2439	0.2470	0.2509	0.2512	0.2518
C₁₆	0.2485	0.2470	0.2524	0.2521	0.2530	0.2524	0.2509	0.2530	0.2428	0.2485	0.2470	0.2524
C₁₇	0.2518	0.2500	0.2518	0.2518	0.2500	0.2506	0.2446	0.2500	0.2458	0.2518	0.2500	0.2518
C₁₈	0.2476	0.2497	0.2497	0.2524	0.2473	0.2497	0.2524	0.2533	0.2509	0.2476	0.2497	0.2497
C₁₉	0.2488	0.2509	0.2494	0.2488	0.2485	0.2506	0.2536	0.2497	0.2506	0.2488	0.2509	0.2494
C₂₁	0.2530	0.2515	0.2503	0.2494	0.2503	0.2467	0.2446	0.2467	0.2527	0.2530	0.2515	0.2503
C₂₂	0.2524	0.2515	0.2488	0.2549	0.2503	0.2512	0.2402	0.2467	0.2512	0.2524	0.2515	0.2488
C₂₃	0.2527	0.2491	0.2494	0.2467	0.2515	0.2506	0.2479	0.2503	0.2506	0.2527	0.2491	0.2494
C₂₄	0.2503	0.2485	0.2509	0.2515	0.2509	0.2497	0.2479	0.2521	0.2485	0.2503	0.2485	0.2509
C₂₅	0.2524	0.2464	0.2503	0.2476	0.2536	0.2503	0.2476	0.2536	0.2491	0.2524	0.2464	0.2503
C₂₆	0.2515	0.2497	0.2512	0.2515	0.2509	0.2512	0.2455	0.2497	0.2464	0.2515	0.2497	0.2512
C₂₇	0.2518	0.2497	0.2515	0.2530	0.2485	0.2467	0.2433	0.2521	0.2503	0.2518	0.2497	0.2515

Criterion in the second layer	Criterion in the third layer
Warhead damage capability (0.6)	Missile hit position (0.1)
	Hole size (0.05)
	Number of penetrating cabins (0.05)
	Range of shock wave（0.07）
	Shock wave overpressure (0.07)
	Pressure duration (0.25)
	Number of fragments (0.07)
	Quality of fragment (0.06)
	Initial velocity of fragments (0.1)
Damage resistance of ship (0.4)	Geometry of the ship (0.06)
	Hull bulkhead structure(0.13)
	Hull deck structure (0.1)
	Special structure (0.05)
	Main material of the ship (0.28)
	Ship stiffener (0.22)
	Welding materials for ship (0.16)

Expert	A₁	A₂	A₃
Expert 1	0.1962	0.1613	0.2496
Expert 2	0.2071	0.1817	0.2376
Expert 3	0.2119	0.1107	0.1523
Expert 4	0.1637	0.1931	0.2025

Case	A₁	A₂	A₃
Assessment value	0.1951	0.1590	0.2068

θ/%	w₁	w₂
−30	0.72	0.28
−20	0.68	0.32
−10	0.64	0.36
0	0.60	0.40
10	0.56	0.44
20	0.52	0.48
30	0.48	0.52