Abstract

Getting access to the state of turbulent flow from limited sensor measurements in engineering systems is a major challenge. Development of technologies to accurately estimate the state of the flow is now possible with the use of machine learning. We present a supervised machine learning technique to reconstruct turbulent vortical structures in a pump sump from sparse surface pressure measurements. For the current flow reconstruction technique, a combination of multilayer perceptron and three-dimensional convolutional neural network is utilized. This technique provides accurate flow estimation from only a few sensor measurements, identifying the presence of adverse vortices. The dependence of the model performance on the amount of training data, the number of input sensors, and the noise levels are investigated. The present machine learning-based flow estimator supports safe operations of pumps and can be extended to a broad range of applications for industrial fluid-based systems.

References

1.
Liu
,
Q.
,
An
,
B.
,
Nohmi
,
M.
,
Obuchi
,
M.
, and
Taira
,
K.
,
2020
, “
Active Flow Control of a Pump-Induced Wall-Normal Vortex With Steady Blowing
,”
ASME J. Fluids Eng.
,
142
(
8
), p.
081202
.10.1115/1.4046692
2.
Brennen
,
C. E.
,
2005
,
Fundamentals of Multiphase Flow
,
Cambridge University Press
, Cambridge, UK.
3.
Brennen
,
C. E.
,
2011
,
Hydrodynamics of Pumps
,
Cambridge University Press
, Cambridge, UK.
4.
Hatano
,
S.
,
Kang
,
D.
,
Kagawa
,
S.
,
Nohmi
,
M.
, and
Yokota
,
K.
,
2014
, “
Study of Cavitation Instabilities in Double-Suction Centrifugal Pump
,”
Int. J. Fluid Mach. Syst.
,
7
(
3
), pp.
94
100
.10.5293/IJFMS.2014.7.3.094
5.
Kang
,
D.
,
Yamazaki
,
S.
,
Kagawa
,
S.
,
An
,
B.
,
Nohmi
,
M.
, and
Yokota
,
K.
,
2019
, “
Flow Characteristics in a V-Shaped Region of a Suction Performance Curve in a Double-Suction Centrifugal Pump
,”
Int. J. Fluid Mach. Syst.
,
12
(
1
), pp.
89
98
.10.5293/IJFMS.2019.12.1.089
6.
Adrian
,
R. J.
, and
Moin
,
P.
,
1988
, “
Stochastic Estimation of Organized Turbulent Structure: Homogeneous Shear Flow
,”
J. Fluid Mech.
,
190
, pp.
531
559
.10.1017/S0022112088001442
7.
Nakamura
,
T.
,
Fukami
,
K.
, and
Fukagata
,
K.
,
2022
, “
Identifying Key Differences Between Linear Stochastic Estimation and Neural Networks for Fluid Flow Regressions
,”
Sci. Rep.
,
12
, p.
3726
.10.1038/s41598-022-07515-7
8.
Chevalier
,
M.
,
Hœpffner
,
J.
,
Bewley
,
T. R.
, and
Henningson
,
D. S.
,
2006
, “
State Estimation in Wall-Bounded Flow Systems. part 2. turbulent Flows
,”
J. Fluid Mech.
,
552
(
-1
), pp.
167
187
.10.1017/S0022112005008578
9.
Colburn
,
C. H.
,
Cessna
,
J. B.
, and
Bewley
,
T. R.
,
2011
, “
State Estimation in Wall-Bounded Flow Systems. Part 3. the Ensemble Kalman Filter
,”
J. Fluid Mech.
,
682
, pp.
289
303
.10.1017/jfm.2011.222
10.
Hemati
,
M. S.
,
Eldredge
,
J. D.
, and
Speyer
,
J. L.
,
2014
, “
Wake Sensing for Aircraft Formation Flight
,”
J. Guid. Control Dyn.
,
37
(
2
), pp.
513
524
.10.2514/1.61114
11.
Le Provost
,
M.
, and
Eldredge
,
J. D.
,
2021
, “
Ensemble Kalman Filter for Vortex Models of Disturbed Aerodynamic Flows
,”
Phys. Rev. Fluids
,
6
(
5
), p.
050506
.10.1103/PhysRevFluids.6.050506
12.
Everson
,
R.
, and
Sirovich
,
L.
,
1995
, “
Karhunen–Loeve Procedure for Gappy Data
,”
J. Opt. Soc. Am.
,
12
(
8
), pp.
1657
1664
.10.1364/JOSAA.12.001657
13.
Bui-Thanh
,
T.
,
Damodaran
,
M.
, and
Willcox
,
K.
,
2004
, “
Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition
,”
AIAA J.
,
42
(
8
), pp.
1505
1516
.10.2514/1.2159
14.
Willcox
,
K.
,
2006
, “
Unsteady Flow Sensing and Estimation Via the Gappy Proper Orthogonal Decomposition
,”
Comput. Fluids
,
35
(
2
), pp.
208
226
.10.1016/j.compfluid.2004.11.006
15.
Murray
,
N. E.
, and
Ukeiley
,
L. S.
,
2006
, “
An Application of Gappy Pod
,”
Exp. Fluids
,
42
(
1
), pp.
79
91
.10.1007/s00348-006-0221-y
16.
Brunton
,
S. L.
,
Noack
,
B. R.
, and
Koumoutsakos
,
P.
,
2020
, “
Machine Learning for Fluid Mechanics
,”
Annu. Rev. Fluid Mech.
,
52
(
1
), pp.
477
508
.10.1146/annurev-fluid-010719-060214
17.
Duraisamy
,
K.
,
2021
, “
Perspectives on Machine Learning-Augmented Reynolds-Averaged and Large Eddy Simulation Models of Turbulence
,”
Phys. Rev. Fluids
,
6
(
5
), p.
050504
.10.1103/PhysRevFluids.6.050504
18.
Callaham
,
J. L.
,
Maeda
,
K.
, and
Brunton
,
S. L.
,
2019
, “
Robust Flow Reconstruction From Limited Measurements Via Sparse Representation
,”
Phys. Rev. Fluids
,
4
(
10
), p.
103907
.10.1103/PhysRevFluids.4.103907
19.
Kramer
,
B.
,
Grover
,
P.
,
Boufounos
,
P.
,
Nabi
,
S.
, and
Benosman
,
M.
,
2017
, “
Sparse Sensing and DMD-Based Identification of Flow Regimes and Bifurcations in Complex Flows
,”
SIAM J. Appl. Dyn. Sys.
,
16
(
2
), pp.
1164
1196
.10.1137/15M104565X
20.
Brenner
,
M. P.
,
Eldredge
,
J. D.
, and
Freund
,
J. B.
,
2019
, “
Perspective on Machine Learning for Advancing Fluid Mechanics
,”
Phys. Rev. Fluids
,
4
(
10
), p.
100501
.10.1103/PhysRevFluids.4.100501
21.
Buzzicotti
,
M.
,
Bonaccorso
,
F.
,
Di Leoni
,
P. C.
, and
Biferale
,
L.
,
2021
, “
Reconstruction of Turbulent Data With Deep Generative Models for Semantic Inpainting From Turb-Rot Database
,”
Phys. Rev. Fluids
,
6
(
5
), p.
050503
.10.1103/PhysRevFluids.6.050503
22.
Fukami
,
K.
,
Fukagata
,
K.
, and
Taira
,
K.
,
2019
, “
Super-Resolution Reconstruction of Turbulent Flows With Machine Learning
,”
J. Fluid Mech.
,
870
, pp.
106
120
.10.1017/jfm.2019.238
23.
Lee
,
S.
, and
You
,
D.
,
2019
, “
Data-Driven Prediction of Unsteady Flow Over a Circular Cylinder Using Deep Learning
,”
J. Fluid Mech.
,
879
, pp.
217
254
.10.1017/jfm.2019.700
24.
Lee
,
S.
, and
You
,
D.
,
2021
, “
Analysis of a Convolutional Neural Network for Predicting Unsteady Volume Wake Flow Fields
,”
Phys. Fluids
,
33
(
3
), p.
035152
.10.1063/5.0042768
25.
Erichson
,
N. B.
,
Mathelin
,
L.
,
Yao
,
Z.
,
Brunton
,
S. L.
,
Mahoney
,
M. W.
, and
Kutz
,
J. N.
,
2020
, “
Shallow Neural Networks for Fluid Flow Reconstruction With Limited Sensors
,”
Proc. Royal Soc. A
,
476
(
2238
), p.
20200097
.10.1098/rspa.2020.0097
26.
Nair
,
N. J.
, and
Goza
,
A.
,
2020
, “
Leveraging Reduced-Order Models for State Estimation Using Deep Learning
,”
J. Fluid Mech.
,
897
, p.
R1
.10.1017/jfm.2020.409
27.
Fukami
,
K.
,
Fukagata
,
K.
, and
Taira
,
K.
,
2021
, “
Machine-Learning-Based Spatio-Temporal Super Resolution Reconstruction of Turbulent Flows
,”
J. Fluid Mech.
,
909
, p.
A9
.10.1017/jfm.2020.948
28.
Leer
,
M.
, and
Kempf
,
A.
,
2021
, “
Fast Flow Field Estimation for Various Applications With a Universally Applicable Machine Learning Concept
,”
Flow Turbul. Comb.
,
107
(
1
), pp.
175
200
.10.1007/s10494-020-00234-x
29.
Fukami
,
K.
,
Maulik
,
R.
,
Ramachandra
,
N.
,
Fukagata
,
K.
, and
Taira
,
K.
,
2021
, “
Global Field Reconstruction From Sparse Sensors With Voronoi Tessellation-Assisted Deep Learning
,”
Nat. Mach. Intell.
,
3
(
11
), pp.
945
951
.10.1038/s42256-021-00402-2
30.
Zhao
,
L.
,
2010
, “
Visualization of Vortices in Pump Sump
,”
J. Visualization Soc. Jpn.
,
30
(
116
), pp.
28
33
.10.3154/jvs.30.28
31.
An
,
B.
,
Liu
,
Q.
,
Taira
,
K.
,
Nohmi
,
M.
, and
Obuchi
,
M.
,
2018
, “
A Research Outlook on Turbulent Vortex Control in Pump Sump
,”
Ebara Tech. Rev.
,
255
, pp.
31
37
.
32.
Yang
,
H. Q.
,
2017
, “
A Computational Fluid Dynamics Study of Swirling Flow Reduction by Using Anti-Vortex Baffle
,”
AIAA
Paper No. 2017-1707.10.2514/6.2017-1707
33.
Weller
,
H. G.
,
Tabor
,
G.
,
Jasak
,
H.
, and
Fureby
,
C.
,
1998
, “
A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques
,”
Comput. Phys.
,
12
(
6
), pp.
620
631
.10.1063/1.168744
34.
Nicoud
,
F.
, and
Ducros
,
F.
,
1999
, “
Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor
,”
Flow Turbul. Combust.
,
62
(
3
), pp.
183
200
.10.1023/A:1009995426001
35.
An
,
B.
,
Liu
,
Q.
,
Nohmi
,
M.
,
Obuchi
,
M.
, and
Taira
,
K.
,
2019
, “
Dynamic Mode Analysis and Control of Vortical Flows in Pump Sumps
,”
APS Division of Fluid Dynamics Meeting Abstracts
, Seattle, WA, pp.
Q27
006
.
36.
Fukami
,
K.
,
Fukagata
,
K.
, and
Taira
,
K.
,
2020
, “
Assessment of Supervised Machine Learning for Fluid Flows
,”
Theor. Comput. Fluid Dyn.
,
34
(
4
), pp.
497
519
.10.1007/s00162-020-00518-y
37.
Hunt
,
J. C. R.
,
Wray
,
A. A.
, and
Moin
,
P.
,
1988
, “
Eddies, Streams, and Convergence Zones in Turbulent Flows
,”
Studying Turbulence Using Numerical Simulation Databases, 2. Proceedings of the 1988 Summer Program
.
38.
Rumelhart
,
D. E.
,
Hinton
,
G. E.
, and
Williams
,
R. J.
,
1986
, “
Learning Representations by Back-Propagation Errors
,”
Nature
,
323
(
6088
), pp.
533
536
.10.1038/323533a0
39.
LeCun
,
Y.
,
Bottou
,
L.
,
Bengio
,
Y.
, and
Haffner
,
P.
,
1998
, “
Gradient-Based Learning Applied to Document Recognition
,”
Proc. IEEE
,
86
(
11
), pp.
2278
2324
.10.1109/5.726791
40.
Wu
,
Z.
,
Pan
,
S.
,
Chen
,
F.
,
Long
,
G.
,
Zhang
,
C.
, and
Philip
,
S. Y.
,
2021
, “
A Comprehensive Survey on Graph Neural Networks
,”
IEEE Trans. Neural Networks Learn. Syst.
,
32
(
1
), pp.
4
24
.10.1109/TNNLS.2020.2978386
41.
Nair
,
V.
, and
Hinton
,
G. E.
,
2010
, “
Rectified Linear Units Improve Restricted Boltzmann Machines
,”
Proceedings of 27th International Conference on Machine Learning,
Haifa, Israel, June, pp.
807
814
.
42.
Morimoto
,
M.
,
Fukami
,
K.
,
Zhang
,
K.
,
Nair
,
A. G.
, and
Fukagata
,
K.
,
2021
, “
Convolutional Neural Networks for Fluid Flow Analysis: Toward Effective Metamodeling and Low Dimensionalization
,”
Theor. Comput. Fluid Dyn.
,
35
(
5
), pp.
633
658
.10.1007/s00162-021-00580-0
43.
Guastoni
,
L.
,
Güemes
,
A.
,
Ianiro
,
A.
,
Discetti
,
S.
,
Schlatter
,
P.
,
Azizpour
,
H.
, and
Vinuesa
,
R.
,
2021
, “
Convolutional-Network Models to Predict Wall-Bounded Turbulence From Wall Quantities
,”
J. Fluid Mech.
,
928
, p.
A27
.10.1017/jfm.2021.812
44.
Kim
,
J.
, and
Lee
,
C.
,
2020
, “
Prediction of Turbulent Heat Transfer Using Convolutional Neural Networks
,”
J. Fluid Mech.
,
882
, p.
A18
.10.1017/jfm.2019.814
45.
Kingma
,
D. P.
, and
Ba
,
J.
,
2014
, “
Adam: A Method for Stochastic Optimization
,” arXiv preprint, arXiv:1412.6980.
46.
Prechelt
,
L.
,
1998
, “
Automatic Early Stopping Using Cross Validation: Quantifying the Criteria
,”
Neural Netw.
,
11
(
4
), pp.
761
767
.10.1016/S0893-6080(98)00010-0
47.
Chong
,
M. S.
,
Perry
,
A. E.
, and
Cantwell
,
B. J.
,
1990
, “
A General Classification of Three-Dimensional Flow Fields
,”
Phys. Fluids A: Fluid Dyn.
,
2
(
5
), pp.
765
777
.10.1063/1.857730
48.
Jeong
,
J.
, and
Hussain
,
F.
,
1995
, “
On the Identification of a Vortex
,”
J. Fluid Mech.
,
285
, pp.
69
94
.10.1017/S0022112095000462
49.
Liu
,
Q.
,
An
,
B.
,
Nohmi
,
M.
,
Obuchi
,
M.
, and
Taira
,
K.
,
2018
, “
Core-Pressure Alleviation for a Wall-Normal Vortex by Active Flow Control
,”
J. Fluid Mech.
,
853
, p.
R1
.10.1017/jfm.2018.629
50.
Taira
,
K.
,
Brunton
,
S. L.
,
Dawson
,
S. T. M.
,
Rowley
,
C. W.
,
Colonius
,
T.
,
McKeon
,
B. J.
,
Schmidt
,
O. T.
,
Gordeyev
,
S.
,
Theofilis
,
V.
, and
Ukeiley
,
L. S.
,
2017
, “
Modal Analysis of Fluid Flows: An Overview
,”
AIAA J.
,
55
(
12
), pp.
4013
4041
.10.2514/1.J056060
51.
Taira
,
K.
,
Hemati
,
M. S.
,
Brunton
,
S. L.
,
Sun
,
Y.
,
Duraisamy
,
K.
,
Bagheri
,
S.
,
Dawson
,
S.
, and
Yeh
,
C.-A.
,
2020
, “
Modal Analysis of Fluid Flows: Applications and Outlook
,”
AIAA J.
,
58
(
3
), pp.
998
1022
.10.2514/1.J058462
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