Detecting acoustic signals in the ocean is crucial for port and coastal security, but existing methods often require informative priors. This paper introduces a new approach that transforms acoustic signal detection into network characterization using a MCN construction method. The method constructs a network representation of the acoustic signal by measuring pairwise correlations at different time scales. It proposes a network spectrum distance method that combines information geometry and graph signal processing theory to characterize these complex networks. By comparing the spectra of two networks, the method quantifies their similarity or dissimilarity, enabling comparisons of multi-scale correlation networks constructed from different time series data and tracking changes in nonlinear dynamics over time. The effectiveness of these methods is substantiated through comprehensive simulations and real-world data collected from the South China Sea. The results illustrate that the proposed approach attains a significant detection probability of over 90% when the signal-to-noise ratio exceeds −18 dB, whereas existing methods require a signal-to-noise ratio of at least −15 dB to achieve a comparable detection probability. This innovative approach holds promising applications in bolstering port security, facilitating coastal operations, and optimizing offshore activities by enabling more efficient detection of weak acoustic signals.
REFERENCES
1.
Albert
,
R.
, and
Barabási
,
A.-L.
(2002
). “
Statistical mechanics of complex networks
,” Rev. Mod. Phys.
74
(1
), 47
–97
.2.
Brockett
,
P. L.
,
Hinich
,
M.
, and
Wilson
,
G. R.
(1987
). “
Nonlinear and non-Gaussian ocean noise
,” J. Acoust. Soc. Am.
82
(4
), 1386
–1394
.3.
Chen
,
Y.
, and
Lin
,
A.
(2021
). “
Weighted link entropy and multiscale weighted link entropy for complex time series
,” Nonlinear Dyn.
105
(1
), 541
–554
.4.
Citi
,
L.
,
Guffanti
,
G.
, and
Mainardi
,
L.
(2014
). “
Rank-based multi-scale entropy analysis of heart rate variability
,” in Proceedings of Computing in Cardiology 2014
, September 7–10, Cambridge, MA (
IEEE
,
New York
), pp. 597
–600
.5.
Cong
,
Y.
,
Fan
,
B.
,
Hou
,
D.
,
Fan
,
H.
,
Liu
,
K.
, and
Luo
,
J.
(2019
). “
Novel event analysis for human-machine collaborative underwater exploration
,” Pattern Recognit.
96
, 106967
.6.
Costa
,
M.
,
Goldberger
,
A. L.
, and
Peng
,
C.-K.
(2002
). “
Multiscale entropy analysis of complex physiologic time series
,” Phys. Rev. Lett.
89
(6
), 068102
.7.
Felice
,
D.
,
Cafaro
,
C.
, and
Mancini
,
S.
(2018
). “
Information geometric methods for complexity
,” Chaos
28
(3
), 032101
.8.
Ferguson
,
E. L.
,
Ramakrishnan
,
R.
,
Williams
,
S. B.
, and
Jin
,
C. T.
(2017
). “
Convolutional neural networks for passive monitoring of a shallow water environment using a single sensor
,” in Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
, March 5–9, New Orleans, LA (
IEEE
,
New York
), pp. 2657
–2661
.9.
Firat
,
U.
, and
Akgül
,
T.
(2013
). “
Spectral estimation of cavitation related narrow-band ship radiated noise based on fractional lower order statistics and multiple signal classification
,” in Proceedings of 2013 OCEANS–San Diego
, September 23–27, San Diego, CA (
IEEE
,
New York
).10.
Gavili
,
A.
, and
Zhang
,
X.-P.
(2017
). “
On the shift operator, graph frequency, and optimal filtering in graph signal processing
,” IEEE Trans. Signal Process.
65
(23
), 6303
–6318
.11.
Grelowska
,
G.
,
Kozaczka
,
E.
,
Kozaczka
,
S.
, and
Szymczak
,
W.
(2013
). “
Underwater noise generated by a small ship in the shallow sea
,” Arch. Acoust.
38
(3
), 351
–356
.12.
Hansen
,
C.
,
Wei
,
Q.
,
Shieh
,
J.-S.
,
Fourcade
,
P.
,
Isableu
,
B.
, and
Majed
,
L.
(2017
). “
Sample entropy, univariate, and multivariate multi-scale entropy in comparison with classical postural sway parameters in young healthy adults
,” Front. Hum. Neurosci.
11
, 206
.13.
Hansen
,
F.
(2006
). “
Trace functions as Laplace transforms
,” J. Math. Phys.
47
(4
), 043504
.14.
Hongwei
,
Z.
,
Wang
,
H.
,
Yongsheng
,
Y.
,
Haiyang
,
Y.
, and
Haitao
,
D.
(2022
). “
Remote passive sonar detection by relative multiscale change entropy
,” IEEE Sens. J.
22
(18
), 18066
–18075
.15.
Jiayu
,
L.
,
Yueke
,
W.
,
Zhiping
,
H.
, and
Zhenkang
,
S.
(1999
). “
Selection of time delay in speech signal phase space reconstruction: Complex autocorrelation method
,” Signal Process.
3
, 220
–22
, available at https://kns.cnki.net/kcms2/article/abstract?v=6Zsqnb4eDBXvQqY6qc9f04QGVfSWTNZmOW5JtgNRnVOo2s4k-QvgbvFnDu-2f5hhsXvGQKTCccV0QWhNPyO9Dp49NK98UwzdoZqrix1zAki_HK9kKPTOlbyyjpbGFTnU&uniplatform=NZKPT&language=CHS (in Chinese).16.
Johnson
,
D.
, and
Sinanovic
,
S.
(2001
). “
Symmetrizing the Kullback–Leibler distance
,” available at https://hdl.handle.net/1911/19969.17.
Lacasa
,
L.
,
Luque
,
B.
,
Ballesteros
,
F.
,
Luque
,
J.
, and
Nuño
,
J. C.
(2008
). “
From time series to complex networks: The visibility graph
,” Proc. Natl. Acad. Sci. U.S.A.
105
(13
), 4972
–4975
.18.
Lake
,
D. E.
,
Richman
,
J. S.
,
Griffin
,
M. P.
, and
Moorman
,
J. R.
(2002
). “
Sample entropy analysis of neonatal heart rate variability
,” Am. J. Physiol. Regul. Integr. Comp. Physiol.
283
(3
), R789
–R797
.19.
Lampert
,
T. A.
, and
O'Keefe
,
S. E.
(2013
). “
On the detection of tracks in spectrogram images
,” Pattern Recognit.
46
(5
), 1396
–1408
.20.
Leroy
,
E. C.
,
Samaran
,
F.
,
Stafford
,
K. M.
,
Bonnel
,
J.
, and
Royer
,
J.-Y.
(2018
). “
Broad-scale study of the seasonal and geographic occurrence of blue and fin whales in the Southern Indian Ocean
,” Endanger. Species Res.
37
, 289
–300
.21.
Malinowski
,
S. J.
, and
Gloza
,
I.
(2002
). “
Underwater noise characteristics of small ships
,” Acta Acust. united Acust.
88
(5
), 718
–721
.22.
Manis
,
G.
,
Aktaruzzaman
,
M.
, and
Sassi
,
R.
(2017
). “
Bubble entropy: An entropy almost free of parameters
,” IEEE Trans. Biomed. Eng.
64
(11
), 2711
–2718
.23.
Masoller
,
C.
,
Hong
,
Y.
,
Ayad
,
S.
,
Gustave
,
F.
,
Barland
,
S.
,
Pons
,
A. J.
,
Gómez
,
S.
, and
Arenas
,
A.
(2015
). “
Quantifying sudden changes in dynamical systems using symbolic networks
,” New J. Phys.
17
(2
), 023068
.24.
Mo
,
H.
, and
Deng
,
Y.
(2019
). “
Identifying node importance based on evidence theory in complex networks
,” Phys. A: Stat. Mech. Appl.
529
, 121538
.25.
Nikias
,
C. L.
, and
Mendel
,
J. M.
(1993
). “
Signal processing with higher-order spectra
,” IEEE Signal Process. Mag.
10
(3
), 10
–37
.26.
Osman
,
A.
,
Nourledin
,
A.
,
El-Sheimy
,
N.
,
Theriault
,
J.
, and
Campbell
,
S.
(2009
). “
Improved target detection and bearing estimation utilizing fast orthogonal search for real-time spectral analysis
,” Meas. Sci. Technol.
20
(6
), 065201
.27.
Pincus
,
S. M.
(1991
). “
Approximate entropy as a measure of system complexity
,” Proc. Natl. Acad. Sci. U.S.A.
88
(6
), 2297
–2301
.28.
Pradhan
,
C.
, and
Gupta
,
A.
(2017
). “
Ship detection using Neyman–Pearson criterion in marine environment
,” Ocean Eng.
143
, 106
–112
.29.
Sadler
,
B. M.
,
Giannakis
,
G. B.
, and
Lii
,
K.-S.
(1994
). “
Estimation and detection in non-Gaussian noise using higher order statistics
,” IEEE Trans. Signal Process.
42
(10
), 2729
–2741
.30.
Shternshis
,
A.
,
Mazzarisi
,
P.
, and
Marmi
,
S.
(2022
). “
Measuring market efficiency: The Shannon entropy of high-frequency financial time series
,” Chaos Solitons Fractals
162
, 112403
.31.
Shuman
,
D. I.
,
Narang
,
S. K.
,
Frossard
,
P.
,
Ortega
,
A.
, and
Vandergheynst
,
P.
(2013
). “
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
,” IEEE Signal Process. Mag.
30
(3
), 83
–98
.32.
Siddagangaiah
,
S.
,
Li
,
Y.
,
Guo
,
X.
,
Chen
,
X.
,
Zhang
,
Q.
,
Yang
,
K.
, and
Yang
,
Y.
(2016
). “
A complexity-based approach for the detection of weak signals in ocean ambient noise
,” Entropy
18
(3
), 101
–114
.33.
Siddagangaiah
,
S.
,
Li
,
Y.
,
Guo
,
X.
, and
Yang
,
K.
(2015
). “
On the dynamics of ocean ambient noise: Two decades later
,” Chaos
25
(10
), 103117
.34.
Sreedavy
,
E.
,
Pradeepa
,
R.
, and
Felix
,
V.
(2009
). “
A novel algorithm for intercept sonar signal detector
,” in Proceedings of the 2009 International Symposium on Ocean Electronics (SYMPOL 2009)
, November 18–20, Cochin, India (
IEEE
,
New York
).35.
Sun
,
J.
,
Yang
,
Y.
,
Xiong
,
N. N.
,
Dai
,
L.
,
Peng
,
X.
, and
Luo
,
J.
(2019
). “
Complex network construction of multivariate time series using information geometry
,” IEEE Trans. Syst. Man. Cybern, Syst.
49
(1
), 107
–122
.36.
Sun
,
X.
,
Small
,
M.
,
Zhao
,
Y.
, and
Xue
,
X.
(2014
). “
Characterizing system dynamics with a weighted and directed network constructed from time series data
,” Chaos
24
(2
), 024402
.37.
Takens
,
F.
(1981
). “
Detecting strange attractors in turbulence
,” in Dynamical Systems and Turbulence, Warwick 1980
(
Springer
,
Berlin
), pp. 366
–381
.38.
Tang
,
M.
,
Rong
,
Y.
,
Zhou
,
J.
, and
Li
,
X. R.
(2019
). “
Information geometric approach to multisensor estimation fusion
,” IEEE Trans. Signal Process.
67
(2
), 279
–292
.39.
Tootooni
,
M. S.
,
Rao
,
P. K.
,
Chou
,
C.-A.
, and
Kong
,
Z. J.
(2018
). “
A spectral graph theoretic approach for monitoring multivariate time series data from complex dynamical processes
,” IEEE Trans. Automat. Sci. Eng.
15
(1
), 127
–144
.40.
Tucker
,
J. D.
, and
Azimi-Sadjadi
,
M. R.
(2011
). “
Coherence-based underwater target detection from multiple disparate sonar platforms
,” IEEE J. Ocean. Eng.
36
(1
), 37
–51
.41.
van der Mheen
,
M.
,
Dijkstra
,
H. A.
,
Gozolchiani
,
A.
,
Den Toom
,
M.
,
Feng
,
Q.
,
Kurths
,
J.
, and
Hernandez-Garcia
,
E.
(2013
). “
Interaction network based early warning indicators for the Atlantic MOC collapse
,” Geophys. Res. Lett.
40
(11
), 2714
–2719
, https://doi.org/10.1002/grl.50515.42.
Vangelista
,
L.
(2017
). “
Frequency shift chirp modulation: The LoRa modulation
,” IEEE Signal Process. Lett.
24
(12
), 1818
–1821
.43.
Waghmare
,
R. G.
,
Nalbalwar
,
S. L.
, and
Das
,
A.
(2012
). “
Transient signal detection on the basis of energy and zero crossing detectors
,” Procedia Eng.
30
, 129
–134
.44.
Wan
,
Y.
,
Roy
,
S.
,
Xue
,
M.
, and
Katragadda
,
V.
(2015
). “
Estimating modes of a complex dynamical network from impulse response data: Structural and graph-theoretic characterizations
,” Int. J. Robust Nonlinear Control
25
(10
), 1438
–1453
.45.
Wang
,
D. J.
,
Jann
,
K.
,
Fan
,
C.
,
Qiao
,
Y.
,
Zang
,
Y.-F.
,
Lu
,
H.
, and
Yang
,
Y.
(2018
). “
Neurophysiological basis of multi-scale entropy of brain complexity and its relationship with functional connectivity
,” Front. Neurosci.
12
, 352
.46.
Wang
,
Z.
,
Yin
,
B.
, and
Yan
,
H.
(2019
). “
Weak signal detection based on pseudo Wigner Ville distribution
,” J. Phys. Conf. Ser.
1176
, 062040
.47.
Wei
,
M.
,
Lin
,
Y.
, and
Chen
,
K. E.
(2020
). “
Study on feeding activity of Litopenaeus vannamei based on passive acoustic detection
,” IEEE Access
8
, 156654
–156662
.48.
Xu
,
R.
,
Zhang
,
K.
,
Xu
,
X.
,
He
,
M.
,
Lu
,
F.
, and
Su
,
B.
(2018
). “
Superhydrophobic WS2-nanosheet-wrapped sponges for underwater detection of tiny vibration
,” Adv. Sci.
5
(4
), 1700655
.49.
Yang
,
Y.
, and
Yang
,
H.
(2008
). “
Complex network-based time series analysis
,” Phys. A: Stat. Mech. Appl.
387
(5–6
), 1381
–1386
.50.
Zhang
,
H.
,
Wang
,
H.
,
Liang
,
X.
,
Yan
,
Y.
, and
Shen
,
X.
(2023
). “
Weighted undirected similarity network construction and application for nonlinear time series detection
,” IEEE Signal Process. Lett.
30
, 728
–732
.51.
Zheng
,
E.
,
Yu
,
H.
,
Chen
,
X.
, and
Sun
,
C.
(2016
). “
Line spectrum detection algorithm based on the phase feature of target radiated noise
,” J. Syst. Eng. Electron.
27
(1
), 72
–80
.© 2023 Acoustical Society of America.
2023
Acoustical Society of America
You do not currently have access to this content.