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Vectorial surrogate modeling approach for multi-failure correlated probabilistic evaluation of turbine rotor

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Abstract

For complex structures like aeroengine turbine rotor, its reliability performance is jointly determined by multiple correlated failure modes. Probabilistic evaluation is an effective way to reveal the output response traits and quantify the structural reliability performance. However, for the requirement of evaluating the multivariate output responses and considering the correlation relationships, the multi-failure correlated probabilistic evaluation often shows the complex characteristics of high-nonlinearity and strong-coupling, leading to the conventional evaluation methods are hard to meet the requirements of accuracy and efficiency. To address this problem, a vectorial surrogate model (VSM) method is proposed by fusing the linkage sampling technique and model updating strategy. First, the linkage sampling technique is developed to build the vectorial sample set and the initial VSM by collaboratively extracting multidimensional input variables and multivariate output responses; moreover, the model updating strategy (MU) is presented to find the optimal undetermined parameters and construct the final VSM by addressing the issues of premature convergence and over-fitting problems. Regarding a typical high-pressure turbine rotor with multiple correlated failure modes (i.e., deformation failure, stress failure, strain failure) as engineering application case, the response distributions, reliability degree, sensitivity degree, correlation relationships for each/all failure modes of turbine rotor are obtained by the proposed method. Through the comparison of methods (direct Monte Carlo simulation, polynomial response surface, random forest, support vector regression, artificial neural network, VSM-I (without MU strategy), VSM-II (with MU strategy)), it is verified that the proposed VSM method can efficiently and accurately accomplish the multi-failure correlated probabilistic evaluation.

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Abbreviations

VSM:

Vectorial surrogate model

MU:

Model updating

VSM-I:

Vectorial surrogate model without MU strategy

VSM-II:

Vectorial surrogate model with MU strategy

RF:

Random forest

SVR:

Support vector regression

ANN:

Artificial neural network

MCS:

Monte Carlo Simulation

QRS:

Quadratic response surface

x :

Input variable

y :

Output response

VS:

Vectorial sample set

Relu:

Rectified linear unit function

I(·):

Identity mapping function

ζ :

Undetermined parameter vector

J(·):

Training performance function

ζ * :

Optimal parameter matrix

w ik :

Connection weight between input level and nonlinear mapping level

w kj :

Connection weight between nonlinear mapping level and result output level

b k :

Threshold of nonlinear mapping level

b j :

Threshold of result output level

m t :

Gradient first-order moment estimation

v t :

Gradient second-order moment estimation

β :

Weight hyper-parameter

E[·]:

Mathematics expectation function

η :

Learning rate factor

− ∇J(ζ):

Direction of negative gradient

ω t :

Weight decay rate

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Acknowledgements

This paper is co-supported by the National Natural Science Foundation of China (Grant 52105136 and 51975028), China Postdoctoral Science Foundation (Grant 2021M690290) and the National Science and Technology Major Project (Grant J2019-IV-0016-0084). The authors would like to thank them.

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Authors and Affiliations

  1. School of Energy and Power Engineering, Beihang University, Beijing, 100191, People’s Republic of China

    Xue-Qin Li & Guang-Chen Bai

  2. Research Institute of Aero-Engine, Beihang University, Beijing, 100191, People’s Republic of China

    Lu-Kai Song

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  1. Xue-Qin Li
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Correspondence to Lu-Kai Song.

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Li, XQ., Song, LK. & Bai, GC. Vectorial surrogate modeling approach for multi-failure correlated probabilistic evaluation of turbine rotor. Engineering with Computers 39, 1885–1904 (2023). https://doi.org/10.1007/s00366-021-01594-2

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