Addressing the issue of uncertainty in calculating the damage effectiveness of aerial maneuvering targets due to the random intersection with warhead fragment clusters formed by projectile proximity explosions, this paper puts forward a numerical calculation method of the aerial maneuvering target damage probability under the intersection between the warhead fragment group and the target with random dwell time sequence (RDTS) characteristics. Leveraging the random scattering characteristics of warhead fragment clusters and incorporating the vulnerability characteristics of the aerial maneuvering target, a model for calculating the probability of hitting and damaging an aerial maneuvering target with a warhead fragment cluster from a single projectile’s explosive is established. Factors related to the random dwell time of the target possibly falling into the effective damage area of the warhead fragment cluster from the projectile’s proximity explosion are introduced, resulting in the development of a model for calculating the damage probability of an aerial maneuvering target under RDTS. In addition, we provide a mathematical description of the statistical characteristics of the probability of damage. Through simulation and example calculation and analysis, the results demonstrate that this method can accurately reflect the actual damage effectiveness of warhead fragment clusters formed by projectile proximity explosion on the aerial maneuvering target in a random scattering state, offering a novel theoretical approach for calculating the damage effectiveness of highly maneuverable targets in the future.

1.
J.
Pazhoohan
,
H.
Beiki
, and
M.
Esfandyari
, “
Experimental investigation and adaptive neural fuzzy inference system prediction of copper recovery from flotation tailings by acid leaching in a batch agitated tank
,”
Int. J. Miner. Metall. Mater.
26
(
5
),
538
546
(
2019
).
2.
Y.
Xu
,
Z.
Cai
,
Y.
Ou
,
W.
Wu
,
P.
Zhao
, and
Z.
Qiao
, “
Current research and development of ammunition damage effect assessment technology
,”
Trans. Beijing Inst. Technol.
41
,
569
578
(
2021
).
3.
Y.
Ebrahimian Ghajari
,
A. A.
Alesheikh
,
M.
Modiri
,
R.
Hosnavi
,
M.
Abbasi
, and
A.
Sharifi
, “
Urban vulnerability under various blast loading scenarios: Analysis using GIS-based multi-criteria decision analysis techniques
,”
Cities
72
,
102
114
(
2018
).
4.
M. H.
Nam
,
K.
Park
,
H. C.
Kim
, and
W. S.
Park
, “
Estimation of damage probability of combat vehicle components based on modeling and simulation
,”
J. Mech. Sci. Technol.
34
,
229
238
(
2020
).
5.
C.-l.
Zhai
and
X.-w.
Chen
, “
Probability damage calculation of building targets under the missile warhead strike
,”
Reliab. Eng. Syst. Saf.
202
,
107030
(
2020
).
6.
K.
Abu Salem
,
G.
Palaia
, and
A. A.
Quarta
, “
Impact of figures of merit selection on hybrid–electric regional aircraft design and performance analysis
,”
Energies
16
,
7881
(
2023
).
7.
S.
Zhang
,
X.
Kong
,
Q.
Fang
, and
Y.
Peng
, “
The maximum penetration depth of hypervelocity projectile penetration into concrete targets: Experimental and numerical investigation
,”
Int. J. Impact Eng.
181
,
104734
(
2023
).
8.
Y.
Guo
,
Z.-M.
Qiu
, and
Y.
Cao
, “
Research on algorithm for fire efficiency of shipborne gun weapon system against single target on Island
,”
Acta Armamentarii
36
,
7
10
(
2015
).
9.
K.
Si
,
X.
Li
,
C.
Guo
,
X.
Gong
, and
Z.
Yao
, “
Research on damage assessment method of fragmentation warhead against airplane targets
,”
J. Ballist.
29
,
52
57
(
2017
).
10.
H. E.
Konokman
,
A.
Kayran
, and
M.
Kaya
, “
Aircraft vulnerability assessment against fragmentation warhead
,”
Aerosp. Sci. Technol.
67
,
215
227
(
2017
).
11.
T.
Tan
,
J.
Dai
,
S.
Lin
,
Y.
Cao
, and
M.
Wang
, “
Influence of prefabricated fragments projectile cabin opening attitude on damage probability and attitude optimization
,”
J. Mech. Sci.Technol.
37
,
3045
3063
(
2023
).
12.
Z.
Xu
,
J.
Xue
,
T.
Liu
,
P.
Zhang
, and
X.
Xie
, “
Equivalent damage study of missile due to energetic fragment warhead
,”
J. Nanjing Univ. Sci. Technol.
44
,
348
353
(
2020
).
13.
W.
Qu
,
Z.
Xu
,
B.
Zhang
, and
Y.
Liu
, “
Battle damage assessment method based on BN-cloud model
,”
Acta Armamentarii
37
,
2075
2084
(
2016
).
14.
H.
Li
,
Y.
Hao
, and
X.
Zhang
, “
Numerical calculation method of target damage effectiveness evaluation under uncertain information of warhead fragments
,”
Mathematics
10
,
1688
(
2022
).
15.
S.
Ma
,
H.
Zhang
, and
G.
Yang
, “
Target threat level assessment based on cloud model under fuzzy and uncertain conditions in air combat simulation
,”
Aerosp. Sci. Technol.
67
,
49
53
(
2017
).
16.
T.
Yao
,
R.
Miao
,
W.
Wang
,
Z.
Li
,
J.
Dong
,
Y.
Gu
, and
X.
Yan
, “
Synthetic damage effect assessment through evidential reasoning approach and neural fuzzy inference: Application in ship target
,”
Chin. J. Aeronaut.
35
,
143
157
(
2022
).
17.
Z.
Yang
,
C.
Wan
,
Q.
Yu
,
J.
Yin
, and
Z.
Yang
, “
A machine learning-based Bayesian model for predicting the duration of ship detention in PSC inspection
,”
Transp. Res. E: Logist. Transp. Rev.
180
,
103331
(
2023
).
18.
P. C.
de Lima Silva
,
H. J.
Sadaei
,
R.
Ballini
, and
F. G.
Guimaraes
, “
Probabilistic forecasting with fuzzy time series
,”
IEEE Trans. Fuzzy Syst.
28
,
1771
1784
(
2020
).
19.
Y.
Yuan
,
Y.-q.
Cai
,
H.-g.
Guo
,
P.-w.
Chen
,
R.
Liu
, and
H.-f.
Wang
, “
Time-sequenced damage behavior of reactive projectile impacting double-layer plates
,”
Def. Technol.
27
,
263
272
(
2023
).
20.
J.
Xue
,
H.
Li
, and
T.
Zeng
, “
Calculation method of damage probability based on hierarchical fragment warhead to flying target
,”
J. Detect. Control
44
,
57
60+67
(
2022
).
21.
H.
Li
,
L.
Lu
,
X.
Zhang
, and
X.
Zhang
, “
Space projectile explosion position parameters measurement method and target damage probability calculation analysis
,”
IEEE Access
9
,
29118
29126
(
2021
).
22.
H.
Li
and
X.
Zhang
, “
A target damage effectiveness assessment mathematical calculation method with uncertain information based on an adaptive fuzzy neural network
,”
Int. J. Intell. Syst.
2023
,
9330296
.
23.
R. I.
Butler
,
M.
Cowan
,
B. W.
Duggin
, and
F. H.
Mathews
, “
Mesh-initiated large area detonators
,”
Rev. Sci. Instrum.
47
(
10
),
1261
1263
(
1976
).
24.
W.
Yang
,
W.
Zhong
,
L.
Zhang
, and
Y.
Jiang
, “
A virtual reality approach to the assessment of damage effectiveness of naval artillery ammunition against unmanned surface vessels
,”
IEEE Access
11
,
93500
93510
(
2023
).
25.
M.
Chen
,
H.
Li
,
Y.
Du
, and
C.
Zhang
, “
The traceability method of electronic transformer calibrators based on time series-weighted correlation degree extension integrating Hilbert phase-shift
,”
Rev. Sci. Instrum.
94
(
1
),
014702
(
2023
).
26.
R.
Zhang
,
Y.
Pei
,
P.
Hou
, and
Y.
Ge
, “
Research on damage evaluation of fragmentation warheads against early-warning aircraft
,”
Trans. Beijing Inst. Technol.
42
,
347
358
(
2022
).
27.
P.
Zheng
,
T.
Yang
, and
B.
Wang
, “
The calculation model for killing probability of fragmentation warhead of missile to air target
,”
J. Ballist.
01
,
45
47
(
2006
).
28.
X.
Chen
,
J.
Wang
,
K.
Tang
,
S.
Lin
, and
Y.
Li
, “
Analysis on the initial velocity field of a multi-layer spherical fragment driven by explosion
,”
J. Vib. Shock
39
,
129
134
(
2020
).
29.
S. S.
Wang
,
Terminal Effects
(
Science Press
,
Beijing
,
2019
).
30.
X.
Zhao
,
X.
Han
,
H.
Wu
, and
Y.
Xu
, “
Applied research on damage effectiveness evaluation of guided explosive bomb
,”
Trans. Beijing Inst. Technol.
39
,
551
557
(
2019
).
31.
C.
Liu
and
Z.
Guo
, “
Killing probability and its statistical property for stationary time series
,”
J. North Univ. China, Nat. Sci. Ed.
29
,
32
37
(
2008
).
32.
C.
Liu
,
J.
Wang
, and
Z.
Guo
, “
A estimation method for kill probability based on random residence time series
,”
Acta Armamentarii
32
,
508
512
(
2011
).
33.
D.
Felix
,
I.
Colwill
, and
E.
Stipidis
, “
Real-time calculation of fragment velocity for cylindrical warheads
,”
Def. Technol.
15
,
264
271
(
2019
).
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