Many fluid dynamic systems exhibit undesirable oscillatory instabilities due to positive feedback between fluctuations in their different subsystems. Thermoacoustic instability, aeroacoustic instability, and aeroelastic instability are some examples. When the fluid flow in the system is turbulent, the approach to such oscillatory instabilities occurs through a universal route characterized by a dynamical regime known as intermittency. In this paper, we extract the peculiar pattern of phase space attractors during the regime of intermittency by constructing recurrence networks corresponding to the phase space topology. We further train a convolutional neural network to classify the periodic and aperiodic structures in the recurrence networks and define a measure that indicates the proximity of the dynamical state to the onset of oscillatory instability. We show that this measure can predict the onset of oscillatory instabilities in three different fluid dynamic systems governed by different physical phenomena.

1.
T.
Poinsot
, “
Prediction and control of combustion instabilities in real engines
,”
Proc. Combust. Inst.
36
,
1
28
(
2017
).
2.
T. C.
Lieuwen
,
Unsteady Combustor Physics
(
Cambridge University Press
,
2012
).
3.
A. P.
Dowling
and
J. E.
Ffowcs Williams
,
Sound and Sources of Sound
(
Horwood
,
1983
).
4.
D.
Rockwell
and
E.
Naudascher
, “
Self-sustained oscillations of impinging free shear layers
,”
Annu. Rev. Fluid Mech.
11
,
67
94
(
1979
).
5.
J.
Panda
, “
An experimental investigation of screech noise generation
,”
J. Fluid Mech.
378
,
71
96
(
1999
).
6.
D.
Middleton
, “
Theoretical and experimental investigations into the acoustic output from ejector flows
,”
J. Sound Vib.
11
,
447
473
(
1970
).
7.
G. A.
Flandro
and
J.
Majdalani
, “
Aeroacoustic instability in rockets
,”
AIAA J.
41
,
485
497
(
2003
).
8.
K. A.
Kurbatskii
and
R. R.
Mankbadi
, “
Review of computational aeroacoustics algorithms
,”
Int. J. Comput. Fluid Dyn.
18
,
533
546
(
2004
).
9.
J. F.
Williams
, “
Aeroacoustics
,”
Annu. Rev. Fluid Mech.
9
,
447
468
(
1977
).
10.
A.
Larsen
, “
Aerodynamics of the Tacoma Narrows Bridge—60 years later
,”
Struct. Eng. Int.
10
,
243
248
(
2000
).
11.
M. H.
Hansen
, “
Aeroelastic instability problems for wind turbines
,”
Wind Energy
10
,
551
577
(
2007
).
12.
G. A.
Richards
,
D. L.
Straub
, and
E. H.
Robey
, “
Passive control of combustion dynamics in stationary gas turbines
,”
J. Propul. Power
19
,
795
810
(
2003
).
13.
J.
Lee
and
D.
Santavicca
, “
Experimental diagnostics for the study of combustion instabilities in lean premixed combustors
,”
J. Propul. Power
19
,
735
750
(
2003
).
14.
B.
Korbahti
,
E.
Kagambage
,
T.
Andrianne
,
N. A.
Razak
, and
G.
Dimitriadis
, “
Subcritical, nontypical and period-doubling bifurcations of a delta wing in a low speed wind tunnel
,”
J. Fluids Struct.
27
,
408
426
(
2011
).
15.
V.
Nair
,
G.
Thampi
, and
R. I.
Sujith
, “
Intermittency route to thermoacoustic instability in turbulent combustors
,”
J. Fluid Mech.
756
,
470
487
(
2014
).
16.
V.
Nair
and
R. I.
Sujith
, “
Precursors to self-sustained oscillations in aeroacoustic systems
,”
Int. J. Aeroacoust.
15
,
312
323
(
2016
).
17.
J.
Venkatramani
,
V.
Nair
,
R. I.
Sujith
,
S.
Gupta
, and
S.
Sarkar
, “
Precursors to flutter instability by an intermittency route: A model free approach
,”
J. Fluids Struct.
61
,
376
391
(
2016
).
18.
I.
Pavithran
,
V. R.
Unni
,
A. J.
Varghese
,
R. I.
Sujith
,
A.
Saha
,
N.
Marwan
, and
J.
Kurths
, “
Universality in the emergence of oscillatory instabilities in turbulent flows
,”
Europhys. Lett.
129
,
24004
(
2020
).
19.
I.
Pavithran
,
V. R.
Unni
,
A. J.
Varghese
,
D.
Premraj
,
R. I.
Sujith
,
C.
Vijayan
,
A.
Saha
,
N.
Marwan
, and
J.
Kurths
, “
Universality in spectral condensation
,”
Sci. Rep.
10
,
17405
(
2020
).
20.
R. I.
Sujith
and
V. R.
Unni
, “
Complex system approach to investigate and mitigate thermoacoustic instability in turbulent combustors
,”
Phys. Fluids
32
,
061401
(
2020
).
21.
V.
Nair
,
G.
Thampi
, and
R. I.
Sujith
, “
Intermittency route to thermoacoustic instability in turbulent combustors
,”
J. Fluid Mech.
756
,
470
487
(
2014
).
22.
V.
Nair
and
R. I.
Sujith
, “
Multifractality in combustion noise: Predicting an impending combustion instability
,”
J. Fluid Mech.
747
,
635
655
(
2014
).
23.
V. R.
Unni
,
A.
Mukhopadhyay
, and
R. I.
Sujith
, “
Online detection of impending instability in a combustion system using tools from symbolic time series analysis
,”
Int. J. Spray Combust. Dyn.
7
,
243
255
(
2015
).
24.
H.
Gotoda
,
Y.
Shinoda
,
M.
Kobayashi
,
Y.
Okuno
, and
S.
Tachibana
, “
Detection and control of combustion instability based on the concept of dynamical system theory
,”
Phys. Rev. E
89
,
022910
(
2014
).
25.
M.
Murugesan
and
R. I.
Sujith
, “
Combustion noise is scale-free: Transition from scale-free to order at the onset of thermoacoustic instability
,”
J. Fluid Mech.
772
,
225
(
2015
).
26.
V.
Godavarthi
,
V. R.
Unni
,
E. A.
Gopalakrishnan
, and
R. I.
Sujith
, “
Recurrence networks to study dynamical transitions in a turbulent combustor
,”
Chaos
27
,
063113
(
2017
).
27.
V.
Nair
,
G.
Thampi
, and
R. I.
Sujith
, “Engineering precursors to forewarn the onset of an impending combustion instability,” in Turbo Expo: Power for Land, Sea, and Air (American Society of Mechanical Engineers, 2014), Vol. 45691, p. V04BT04A005.
28.
V.
Godavarthi
,
S. A.
Pawar
,
V. R.
Unni
,
R. I.
Sujith
,
N.
Marwan
, and
J.
Kurths
, “
Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor
,”
Chaos
28
,
113111
(
2018
).
29.
M.
Quade
,
T.
Isele
, and
M.
Abel
, “
Machine learning control—Explainable and analyzable methods
,”
Physica D
412
,
132582
(
2020
).
30.
M.
Schmidt
and
H.
Lipson
, “
Distilling free-form natural laws from experimental data
,”
Science
324
,
81
85
(
2009
).
31.
H. U.
Voss
,
P.
Kolodner
,
M.
Abel
, and
J.
Kurths
, “
Amplitude equations from spatiotemporal binary-fluid convection data
,”
Phys. Rev. Lett.
83
,
3422
(
1999
).
32.
U.
Sengupta
,
G.
Waxenegger-Wilfing
,
J.
Martin
,
J.
Hardi
, and
M.
Juniper
, “
Avoiding high-frequency thermoacoustic instabilities in liquid propellant rocket engines using Bayesian deep learning
,”
Bull. Amer. Phys. Soc.
65
,
1
(
2020
).
33.
T.
Hachijo
,
H.
Gotoda
,
T.
Nishizawa
, and
J.
Kazawa
, “
Experimental study on early detection of cascade flutter in turbo jet fans using combined methodology of symbolic dynamics, dynamical systems theory, and machine learning
,”
J. Appl. Phys.
127
,
234901
(
2020
).
34.
T.
Kobayashi
,
S.
Murayama
,
T.
Hachijo
, and
H.
Gotoda
, “
Early detection of thermoacoustic combustion instability using a methodology combining complex networks and machine learning
,”
Phys. Rev. Appl.
11
,
064034
(
2019
).
35.
C.
Bhattacharya
,
J.
O’Connor
, and
A.
Ray
, “
Data-driven detection and early prediction of thermoacoustic instability in a multi-nozzle combustor
,”
Combust. Sci. Technol.
(published online,
2020
).
36.
S.
Mondal
,
N. F.
Ghalyan
,
A.
Ray
, and
A.
Mukhopadhyay
, “
Early detection of thermoacoustic instabilities using hidden Markov models
,”
Combust. Sci. Technol.
191
,
1309
1336
(
2018
).
37.
M.
Raghunathan
,
N. B.
George
,
V. R.
Unni
,
P. R.
Midhun
,
K. V.
Reeja
, and
R. I.
Sujith
, “
Multifractal analysis of flame dynamics during transition to thermoacoustic instability in a turbulent combustor
,”
J. Fluid Mech.
888
,
A14
(
2020
).
38.
S. H.
Strogatz
,
Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering
(
CRC Press
,
2018
).
39.
H. D. I.
Abarbanel
,
R.
Brown
,
J. J.
Sidorowich
, and
L. S.
Tsimring
, “
The analysis of observed chaotic data in physical systems
,”
Rev. Mod. Phys.
65
,
1331
1392
(
1993
).
40.
L.
Cao
, “
Practical method for determining the minimum embedding dimension of a scalar time series
,”
Physica D
110
,
43
50
(
1997
).
41.
M.
Bastian
,
S.
Heymann
, and
M.
Jacomy
, “Gephi: An open source software for exploring and manipulating networks,” in Proceedings of the Third International Conference on Web and Social Media (ICWSM 2009), San Jose, CA, 17–20 May 2009 (AAAI, 2009).
42.
K.
O’Shea
and
R.
Nash
, “An introduction to convolutional neural networks,” arXiv:1511.08458 (2015).
43.
Y.
Lecun
,
L.
Bottou
,
Y.
Bengio
, and
P.
Haffner
, “
Gradient-based learning applied to document recognition
,”
Proc. IEEE
86
,
2278
2324
(
1998
).
44.
T.
Liu
,
S.
Fang
,
Y.
Zhao
,
P.
Wang
, and
J.
Zhang
, “Implementation of training convolutional neural networks,” arXiv:1506.01195 (2015).
45.
S. L.
Brunton
,
B. R.
Noack
, and
P.
Koumoutsakos
, “
Machine learning for fluid mechanics
,”
Annu. Rev. Fluid Mech.
52
,
477
508
(
2020
).
46.
A.
Krizhevsky
,
I.
Sutskever
, and
G. E.
Hinton
, “ImageNet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems 25, edited by F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger (Curran Associates, Inc., 2012), pp. 1097–1105.
47.
D.
Scherer
,
A.
Müller
, and
S.
Behnke
, “Evaluation of pooling operations in convolutional architectures for object recognition,” in International Conference on Artificial Neural Networks (Springer, 2010), pp. 92–101.
48.
A.
Krizhevsky
,
I.
Sutskever
, and
G. E.
Hinton
, “
Imagenet classification with deep convolutional neural networks
,”
Adv. Neural Inf. Process. Syst.
25
,
1097
1105
(
2012
).
49.
P.-T.
De Boer
,
D. P.
Kroese
,
S.
Mannor
, and
R. Y.
Rubinstein
, “
A tutorial on the cross-entropy method
,”
Ann. Oper. Res.
134
,
19
67
(
2005
).
50.
D. P.
Kingma
and
J.
Ba
, “Adam: A method for stochastic optimization,” arXiv:1412.6980 (2017).
51.
J.
Wu
, “Introduction to convolutional neural networks,” National Key Lab for Novel Software Technology, Nanjing University, China, Vol. 5, p. 23, 2017.
You do not currently have access to this content.