Abstract

The conventional iterative optimization of turbine blades using computer-aided engineering simulations is resource-intensive, with high costs and time demands, as well as significant challenges in computational requirements and data management. The three-dimensional (3D) simulation data generated from computational fluid dynamics (CFD) and finite element analysis (FEA) for various blade geometries can range from hundreds of gigabytes to multiple terabytes, complicating long-term storage and access. To address this, we propose a machine learning-based methodology for data reduction and prediction of 3D surface field data. Our approach involves developing a convolutional variational auto-encoder (VAE), consisting of an encoder and a decoder. The encoder compresses the input data into a representation of reduced dimensionality in a latent space, while the decoder reconstructs the data from this latent space back to its original form. This significantly reduces the amount of stored data, facilitating long-term use. Additionally, we train a fully connected feedforward multilayer perceptron (MLP) to map geometry parameters, which generate blade variations, to the latent space. By combining the MLP with the VAE's trained decoder, we create our proposed multilayer perceptron–variational auto-encoder (MLP–VAE) hybrid model capable of predicting surface field data for new, unseen blade geometries. The MLP–VAE generates latent representations and surface field results with high accuracy (>97%) and without additional computational costs, offering a highly efficient and scalable solution for turbine blade optimization.

References

1.
Poullikkas
,
A.
,
2005
, “
An Overview of Current and Future Sustainable Gas Turbine Technologies
,”
Renewable Sustainable Energy Rev.
,
9
(
5
), pp.
409
443
.10.1016/j.rser.2004.05.009
2.
Saravanamuttoo
,
H. I. H.
,
Rogers
,
G. F. C.
,
Cohen
,
H.
,
Straznicky
,
P.
, and
Nix
,
A. C.
,
2017
,
Gas Turbine Theory
, 7th ed.,
Pearson Education
,
Harlow, UK
.
3.
Ahmadi
,
P.
, and
Dincer
,
I.
,
2011
, “
Thermodynamic and Exergoenvironmental Analyses, and Multi-Objective Optimization of a Gas Turbine Power Plant
,”
Appl. Therm. Eng.
,
31
(
14–15
), pp.
2529
2540
.10.1016/j.applthermaleng.2011.04.018
4.
Talya
,
S. S.
,
Rajadas
,
J. N.
, and
Chattopadhyay
,
A.
,
2000
, “
Multidisciplinary Optimization for Gas Turbine Airfoil Design
,”
Inverse Probl. Eng.
,
8
(
3
), pp.
283
308
.10.1080/174159700088027731
5.
Pierret
,
S.
, and
Van den Braembussche
,
R. A.
,
1999
, “
Turbomachinery Blade Design Using a Navier–Stokes Solver and Artificial Neural Network
,”
ASME J. Turbomach.
,
121
(
2
), pp.
326
332
.10.1115/1.2841318
6.
Wang
,
Q.
,
Yang
,
L.
, and
Rao
,
Y.
,
2021
, “
Establishment of a Generalizable Model on a Small-Scale Dataset to Predict the Surface Pressure Distribution of Gas Turbine Blades
,”
Energy
,
214
, p.
118878
.10.1016/j.energy.2020.118878
7.
Du
,
Q.
,
Li
,
Y.
,
Yang
,
L.
,
Liu
,
T.
,
Zhang
,
D.
, and
Xie
,
Y.
,
2022
, “
Performance Prediction and Design Optimization of Turbine Blade Profile With Deep Learning Method
,”
Energy
,
254
, p.
124351
.10.1016/j.energy.2022.124351
8.
Zhang
,
C.
, and
Janeway
,
M.
,
2022
, “
Optimization of Turbine Blade Aerodynamic Designs Using CFD and Neural Network Models
,”
Int. J. Turbomach., Propul. Power
,
7
(
3
), p.
20
.10.3390/ijtpp7030020
9.
Bank
,
D.
,
Koenigstein
,
N.
, and
Giryes
,
R.
,
2023
, “
Autoencoders
,”
Machine Learning for Data Science Handbook: Data Mining and Knowledge Discovery Handbook
,
L.
Rokach
,
O.
Maimon
, and
E.
Shmueli
, eds.,
Springer International Publishing
,
Cham, Switzerland
, pp.
353
374
.
10.
Rywik
,
M.
,
Zimmermann
,
A.
,
Eder
,
A. J.
,
Scoletta
,
E.
, and
Polifke
,
W.
,
2024
, “
Spatially Resolved Modeling of the Nonlinear Dynamics of a Laminar Premixed Flame With a Multilayer Perceptron–Convolution Autoencoder Network
,”
ASME J. Eng. Gas Turbines Power
,
146
(
6
), p.
061009
.10.1115/1.4063788
11.
Liu
,
G.
,
Li
,
R.
,
Zhou
,
X.
,
Sun
,
T.
, and
Zhang
,
Y.
,
2023
, “
Reconstruction and Fast Prediction of 3D Heat and Mass Transfer Based on a Variational Autoencoder
,”
Int. Commun. Heat Mass Transfer
,
149
, p.
107112
.10.1016/j.icheatmasstransfer.2023.107112
12.
Durakovic
,
B.
,
2017
, “
Design of Experiments Application, Concepts, Examples: State of the Art
,”
Period. Eng. Nat. Sci.
,
5
(
3
), pp.
421
439
.10.21533/pen.v5i3.145
13.
Siemens Energy Customer Support Center
,
2023
, “
We Power the World With Innovative Gas Turbines: Siemens Energy Gas Turbine Portfolio
,” Siemens Energy, Berlin, Germany, accessed Nov. 13, 2024, https://www.siemens-energy.com/global/en/home/products-services/product-offerings/gas-turbines.html
14.
Han
,
J. C.
,
Dutta
,
S.
, and
Ekkad
,
S.
,
2013
,
Gas Turbine Heat Transfer and Cooling Technology
, 2nd ed.,
CRC Press (Taylor & Francis Group)
,
Boca Raton, FL
.
15.
Alonzo-García
,
A.
,
Gutiérrez-Torres
,
C. d. C.
, and
Jiménez-Bernal
,
J. A.
,
2016
, “
Computational Fluid Dynamics in Turbulent Flow Applications
,”
Numerical Simulation
,
R.
Lopez-Ruiz
, ed.,
IntechOpen
,
Rijeka, Croatia
, pp.
315
337
.
16.
Oñate
,
E.
,
2009
,
Structural Analysis With the Finite Element Method. Linear Statics
(Lecture Notes on Numerical Methods in Engineering and Sciences, Vol. 1),
Springer Dordrecht
,
Barcelona, Spain
.
17.
Diwekar
,
U. M.
, and
Kalagnanam
,
J. R.
,
1997
, “
Efficient Sampling Technique for Optimization Under Uncertainty
,”
AIChE J.
,
43
(
2
), pp.
440
447
.10.1002/aic.690430217
18.
Mahajan
,
A.
, and
Stefko
,
G.
,
1993
, “
An Iterative Multidisciplinary Analysis for Rotor Blade Shape Determination
,”
AIAA
Paper No. 93-2085.10.2514/6.93-2085
19.
Zhou
,
D.
,
Lu
,
Z.
,
Guo
,
T.
, and
Chen
,
G.
,
2021
, “
Aeroelastic Prediction and Analysis for a Transonic Fan Rotor With the ‘Hot’ Blade Shape
,”
Chin. J. Aeronaut.
,
34
(
7
), pp.
50
61
.10.1016/j.cja.2020.10.018
20.
Meher-Homji
,
C. B.
, and
Gabriles
,
G.
,
1998
, “
Gas Turbine Blade Failures—Causes, Avoidance, and Troubleshooting
,”
Proceedings of the 27th Turbomachinery Symposium (Texas A&M University)
,
Houston, TX
, Sept. 22–24, pp.
129
180
.https://oaktrust.library.tamu.edu/items/b2699108-8177-487c-9fdc-fa0a27be95f1
21.
Illal
,
V. M.
, and
Bandi
,
P. B. R.
,
2018
, “
Evaluation of Stress Intensity Factor for Turbine Blade Using Finite Element Method
,”
Int. J. Adv. Res., Ideas Innovations Technol.
,
4
(
3
), pp.
728
738
.
22.
Yoru
,
Y.
,
Karakoc
,
T.
, and
Hepbasli
,
A.
,
2009
, “
Application of Artificial Neural Network (ANN) Method to Exergetic Analyses of Gas Turbines
,”
Proceedings of the International Symposium on Heat Transfer in Gas Turbine Systems
,
Antalya, Turkey
, Aug. 9–14, pp.
715
718
.10.1615/ICHMT.2009.HeatTransfGasTurbSyst.580
23.
Lamont
,
W. G.
,
Roa
,
M.
, and
Lucht
,
R. P.
,
2014
, “
Application of Artificial Neural Networks for the Prediction of Pollutant Emissions and Outlet Temperature in a Fuel-Staged Gas Turbine Combustion Rig
,”
ASME
Paper No. GT2014-25030.10.1115/GT2014-25030
24.
Hinton
,
G. E.
, and
Salakhutdinov
,
R. R.
,
2006
, “
Reducing the Dimensionality of Data With Neural Networks
,”
Science
,
313
(
5786
), pp.
504
507
.10.1126/science.1127647
25.
Berthelot
,
D.
,
Raffel
,
C.
,
Roy
,
A.
, and
Goodfellow
,
I.
,
2019
, “
Understanding and Improving Interpolation in Autoencoders Via an Adversarial Regularizer
,” Proceedings of the Seventh International Conference on Learning Representations (
ICLR
),
New Orleans, LA
, May 6–9, pp.
1
20
.https://colinraffel.com/publications/iclr2019understanding.pdf
26.
Kingma
,
D. P.
, and
Welling
,
M.
,
2014
, “
Auto-Encoding Variational Bayes
,” Proceedings of the Second International Conference on Learning Representations (
ICLR
),
Banff, AB, Canada
, Apr. 14–16, pp.
1
14
.https://arxiv.org/pdf/1312.6114
27.
Virtanen
,
P.
,
Gommers
,
R.
,
Oliphant
,
T. E.
,
Haberland
,
M.
,
Reddy
,
T.
,
Cournapeau
,
D.
,
Burovski
,
E.
, et al.,
2020
, “
SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python
,”
Nat. Methods
,
17
(
3
), pp.
261
272
.10.1038/s41592-019-0686-2
28.
Rao
,
S.
,
Poojary
,
P.
,
Somaiya
,
J.
, and
Mahajan
,
P.
,
2020
, “
A Comparative Study Between Various Preprocessing Techniques for Machine Learning
,”
Int. J. Eng. Appl. Sci. Technol.
,
5
(
3
), pp.
431
438
.
29.
Abadi
,
M.
,
Agarwal
,
A.
,
Barham
,
P.
,
Brevdo
,
E.
,
Chen
,
Z.
,
Citro
,
C.
,
Corrado
,
G. S.
, et al.,
2016
, “
TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems
,” Computing Research Repository.https://dblp.org/rec/journals/corr/AbadiABBCCCDDDG16.html
30.
Kingma
,
D. P.
, and
Ba
,
J.
,
2015
, “
Adam: A Method for Stochastic Optimization
,”
Proceedings of the Third International Conference on Learning Representations
(
ICLR
),
San Diego, CA
, May 7–9.https://www.researchgate.net/publication/269935079_Adam_A_Method_for_Stochastic_Optimization
31.
Kaur
,
J.
, and
Jyoti
,
D.
,
2011
, “
Image Quality Assessment Techniques pn Spatial Domain
,”
Int. J. Comput. Sci. Technol.
,
2
(
3
), pp.
177
184
.https://www.ijcst.com/vol23/1/sasivarnan.pdf
32.
Li
,
L.
,
Jamieson
,
K.
,
DeSalvo
,
G.
,
Rostamizadeh
,
A.
, and
Talwalkar
,
A.
,
2017
, “
Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization
,”
J. Mach. Learn. Res.
,
18
(
1
), pp.
6765
6816
.https://jmlr.org/papers/volume18/16-558/16-558.pdf
33.
Goodfellow
,
I. J.
,
Bengio
,
Y.
, and
Courville
,
A.
,
2016
,
Deep Learning
,
MIT Press
,
Cambridge, MA
.
34.
Parsania
,
P.
, and
Virparia
,
P.
,
2016
, “
A Comparative Analysis of Image Interpolation Algorithms
,”
Int. J. Adv. Res. Comput. Commun. Eng.
,
5
(
1
), pp.
29
34
.10.17148/IJARCCE.2016.5107
35.
Li
,
W.
,
Lu
,
L.
,
Xie
,
X.
, and
Yang
,
M.
,
2017
, “
A Novel Extension Algorithm for Optimized Latin Hypercube Sampling
,”
J. Stat. Comput. Simul.
,
87
(
13
), pp.
2549
2559
.10.1080/00949655.2017.1340475
You do not currently have access to this content.