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Research Papers

Mistuning Identification of Integrally Bladed Disks With Cascaded Optimization and Neural Networks

[+] Author and Article Information
Mehmet Ersin Yumer

e-mail: meyumer@cmu.edu

Ender Cigeroglu

e-mail: ender@metu.edu.tr

H. Nevzat Özgüven

Fellow ASME
e-mail: ozguven@metu.edu.tr
Department of Mechanical Engineering,
Middle East Technical University,
Ankara, 06800Turkey

1Present address: Mechanical Engineering Department of Carnegie Mellon University, Pittsburgh, PA.

2Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December 12, 2012; final manuscript received February 2, 2012; published online March 25, 2013. Editor: David Wisler.

J. Turbomach 135(3), 031008 (Mar 25, 2013) (9 pages) Paper No: TURBO-11-1259; doi: 10.1115/1.4006667 History: Revised February 02, 2012; Received December 12, 2012

Mistuning affects forced response of bladed disks drastically; therefore, its identification plays an essential role in the forced response analysis of bladed disk assemblies. Forced response analysis of mistuned bladed disk assemblies has drawn wide attention of researchers but there are a very limited number of studies dealing with identification of mistuning, especially if the component under consideration is an integrally bladed disk (blisk). This paper presents two new methods to identify mistuning of a bladed disk from the assembly modes via utilizing cascaded optimization and neural networks. It is assumed that a tuned mathematical model of the blisk under consideration is readily available, which is always the case for today’s realistic bladed disk assemblies. In the first method, a data set of selected mode shapes and natural frequencies is created by a number of simulations performed by mistuning the tuned mathematical model randomly. A neural network created by considering the number of modes, is then trained with this data set. Upon training the network, it is used to identify mistuning of the rotor from measured data. The second method further improves the first one by using it as a starting point of an optimization routine and carries out an optimization to identify mistuning. To carry out identification analysis by means of the proposed methods, there are no limitations on the number of modes or natural frequencies to be used. Thus, unlike existing mistuning identification methods they are suitable for incomplete data as well. Moreover, since system modes are used rather than blade alone counterparts, the techniques are ready to be used for analysis of blisks. Case studies are performed to demonstrate the capabilities of the new methods by using two different mathematical models to create training data sets a lumped-parameter model and a relatively realistic reduced order model. Throughout the case studies, the effects of using incomplete mode families and random errors in assembly modes are investigated. The results show that, the proposed method utilizing cascaded optimization and neural networks can identify mistuning parameters of a realistic blisk system with an exceptional accuracy even in the presence of incomplete and noisy test data.

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Figures

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Fig. 1

Lumped parameter blisk model

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Fig. 2

Neural network configuration

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Fig. 3

Mean square error progress

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Fig. 4

Comparison of actual and identified mistuning

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Fig. 5

Actual (), identified from noise free data (), identified from noisy data () mode shapes. Numbers from left to right (black, red, and green numbers) correspond to mode shape number, MAC between actual and noise-free-identified mode shapes, and MAC between actual and noisy-identified mode shapes, respectively.

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Fig. 6

Mean square error progress of injection training

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Fig. 7

Comparison of actual and identified mistuning

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Fig. 8

Actual (), identified with Network-STD (), identified with Network-INJ () mode shapes. Numbers from left to right (black, red, and green numbers) correspond to mode shape number, MAC between actual and Network-STD-identified mode shapes, and MAC between actual and Network-INJ-identified mode shapes, respectively.

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Fig. 9

Flow chart of NetID and OptID

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Fig. 10

Sector Mesh of the 24-bladed Blisk

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Fig. 11

Mean square error progress

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Fig. 12

CDF of absolute error

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Fig. 13

Actual and network identified mistuning with optimization bounds

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Fig. 14

Comparison of NetID and OptID Identification

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Fig. 15

Actual (), identified with NetID (), identified with OptID () mode shapes. Numbers from left to right (black, red, and green numbers) correspond to mode shape number, MAC between actual and NetID-identified mode shapes, and MAC between actual and OptID-identified mode shapes, respectively.

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