Abstract

This paper presents an efficient methodology to build a modal solution emulator for the probabilistic study of geometrically mistuned bladed rotors by using the newly developed localized-Galerkin multifidelity (LGMF) modeling and eigensolution reanalysis (ER) with the symmetric successive matrix inversion (SSMI) methods. The key idea of the mistuned blade emulator is to establish a reduced functional relationship between the stochastic geometric variations and the disturbed modal responses. The prediction accuracy of an emulator generally depends on how many training samples of modal solutions are available and how well the potential modal switching due to stochastic mistuning is captured. To reduce the computational costs of generating training samples without sacrificing accuracy, this paper introduces the collaborative framework of the new approaches of multifidelity (MF) modeling and ER. The proposed framework is demonstrated for its computational benefits with several numerical examples including the point-cloud scanned mistuned blade problem.

References

References
1.
Lee
,
S.-Y.
,
Castanier
,
M. P.
, and
Pierre
,
C.
,
2005
, “
Assessment of Probabilistic Methods for Mistuned Bladed Disk Vibration
,”
AIAA
Paper No. 2005-1990.10.2514/6.2005-1990
2.
Brown
,
J. M.
, and
Grandhi
,
R. V.
,
2008
, “
Reduced-Order Model Development for Airfoil Forced Response
,”
Int. J. Rotating Mach.
,
2008
, p.
387828
.10.1155/2008/387828
3.
Henry
,
E. B.
,
Brown
,
J. M.
, and
Slater
,
J. C.
,
2015
, “
A Fleet Risk Prediction Methodology for Mistuned IBRs Using Geometric Mistuning Models
,”
AIAA
Paper No. 2015-1144.10.2514/6.2015-1144
4.
Henry
,
E. B.
,
Brown
,
J. M.
,
Beck
,
J. A.
, and
Kaszynski
,
A. A.
,
2017
, “
Mistuned Rotor Reduced Order Modeling With Surrogate-Modeled Airfoil Substructures
,”
AIAA
Paper No. 2017-1600.10.2514/6.2017-1600
5.
Peherstorfer
,
B.
,
Willcox
,
K.
, and
Gunzburger
,
M.
,
2016
, “
Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
,” ACDL, Massachusetts Institute of Technology, Boston, MA, Report No. TR16-1.
6.
Gano
,
S. E.
,
Renaud
,
J. E.
,
Martin
,
J. D.
, and
Simpson
,
T. W.
,
2005
, “
Update Strategies for Kriging Models for Using in Variable Fidelity Optimization
,”
AIAA
Paper No. 2005–2057.10.2514/6.2005-2057
7.
Eldred
,
M. S.
,
Giunta
,
A. A.
,
Collis
,
S. S.
,
Alexandrov
,
N. A.
, and
Lewis
,
R. M.
,
2004
, “
Second-Order Corrections for Surrogate-Based Optimization With Model Hierarchies
,”
AIAA
Paper No. 2004-4457.10.2514/6.2004-4457
8.
Kennedy
,
M. C.
, and
O'Hagan
,
A.
,
2001
, “
Bayesian Calibration of Computer Models
,”
J. R. Stat. Soc.: Ser. B
,
63
(
3
), pp.
425
464
.10.1111/1467-9868.00294
9.
Qian
,
P. Z.
, and
Wu
,
C. J.
,
2008
, “
Bayesian Hierarchical Modeling for Integrating Low-Accuracy and High-Accuracy Experiments
,”
Technometrics
,
50
(
2
), pp.
192
204
.10.1198/004017008000000082
10.
Han
,
Z.-H.
,
Görtz
,
S.
, and
Zimmermann
,
R.
,
2013
, “
Improving Variable-Fidelity Surrogate Modeling Via Gradient-Enhanced Kriging and a Generalized Hybrid Bridge Function
,”
Aerosp. Sci. Technol.
,
25
(
1
), pp.
177
189
.10.1016/j.ast.2012.01.006
11.
Bickford
,
W. B.
,
1987
, “
An Improved Computational Technique for Perturbations of the Generalized Symmetric Linear Algebraic Eigenvalue Problem
,”
Int. J. Numer. Methods Eng.
,
24
(
3
), pp.
529
541
.10.1002/nme.1620240305
12.
Eldred
,
M. S.
,
Lerner
,
P. B.
, and
Anderson
,
W. J.
,
1992
, “
Higher Order Eigenpair Perturbations
,”
AIAA J.
,
30
(
7
), pp.
1870
1876
.10.2514/3.11149
13.
Kirsch
,
U.
,
2003
, “
Approximate Vibration Reanalysis of Structures
,”
AIAA J.
,
41
(
3
), pp.
504
511
.10.2514/2.1973
14.
Chen
,
S. H.
,
Wu
,
X. M.
, and
Yang
,
Z. J.
,
2006
, “
Eigensolution Reanalysis of Modified Structures Using Epsilon‐Algorithm
,”
Int. J. Numerical Methods Eng.
,
66
(
13
), pp.
2115
2130
.10.1002/nme.1612
15.
Kashiwagi
,
M.
,
2009
, “
A Numerical Method for Eigensolution of Locally Modified Systems Based on the Inverse Power Method
,”
Finite Elem. Anal. Des.
,
45
(
2
), pp.
113
120
.10.1016/j.finel.2008.07.009
16.
Sherman
,
J.
, and
Morrison
,
W. J.
,
1950
, “
Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix
,”
Ann. Math. Stat.
,
21
(
1
), pp.
124
127
.10.1214/aoms/1177729893
17.
Bae
,
H. R.
,
Grandhi
,
R. V.
, and
Canfield
,
R. A.
,
2004
, “
Successive Matrix Inversion Method for Reanalysis of Engineering Structural Systems
,”
AIAA J.
,
42
(
8
), pp.
1529
1535
.10.2514/1.4715
18.
Bae
,
H.-R.
,
Grandhi
,
R. V.
, and
Canfield
,
R. A.
,
2006
, “
Accelerated Engineering Design Optimization Using Successive Matrix Inversion Method
,”
Int. J. Numerical Methods Eng.
,
66
(
9
), pp.
1361
1377
.10.1002/nme.1545
19.
Clark
,
D. L.
, and
Bae
,
H.
, “
Non-Deterministic Kriging Framework for Responses With Mixed Uncertainty
,”
AIAA
Paper No. 2017-0593.10.2514/6.2017-0593
20.
Bae
,
H.
,
Clark
,
D. L.
,
Deaton
,
J. D.
, and
Forster
,
E. E.
,
2019
, “
Multi-Fidelity Modeling Using Non-Deterministic Localized-Galerkin Approach
,”
AIAA
Paper No. 2019-0000.10.2514/6.2019-0000
21.
Van der Vorst
,
H. A.
,
1992
, “
Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
,”
SIAM J. Sci. Stat. Comput.
,
13
(
2
), pp.
631
644
.10.1137/0913035
22.
Saad
,
Y.
,
1988
, “
Projection and Deflation Method for Partial Pole Assignment in Linear State Feedback
,”
IEEE Trans. Autom. Control
,
33
(
3
), pp.
290
297
.10.1109/9.406
You do not currently have access to this content.