Digital twin-assisted gearbox dynamic model updating toward fault diagnosis

doi:10.1007/s11465-023-0748-0

Frontiers of Mechanical Engineering

2023, Vol. 18

Issue (2): 32 https://doi.org/10.1007/s11465-023-0748-0

本期目录

Digital twin-assisted gearbox dynamic model updating toward fault diagnosis

Jingyan XIA¹, Ruyi HUANG^2,³, Yixiao LIAO¹, Jipu LI¹, Zhuyun CHEN^1,³, Weihua LI^1,^2,³(

)

¹. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China
². Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, Guangzhou 511442, China
³. Guangdong Artificial Intelligence and Digital Economy Laboratory (Guangzhou), Guangzhou 510335, China

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Abstract：

One of the core challenges of intelligent fault diagnosis is that the diagnosis model requires numerous labeled training datasets to achieve satisfactory performance. Generating training data using a virtual model is a potential solution for addressing such a problem, and the construction of a high-fidelity virtual model is fundamental and critical for data generation. In this study, a digital twin-assisted dynamic model updating method for fault diagnosis is thus proposed to improve the fidelity and reliability of a virtual model, which can enhance the generated data quality. First, a virtual model is established to mirror the vibration response of a physical entity using a dynamic modeling method. Second, the modeling method is validated through a frequency analysis of the generated signal. Then, based on the signal similarity indicator, a physical–virtual signal interaction method is proposed to dynamically update the virtual model in which parameter sensitivity analysis, surrogate technique, and optimization algorithm are applied to increase the efficiency during the model updating. Finally, the proposed method is successfully applied to the dynamic model updating of a single-stage helical gearbox; the virtual data generated by this model can be used for gear fault diagnosis.

Key words： digital twin gearbox model construction model updating physical–virtual interaction

收稿日期: 2022-10-20 出版日期: 2023-07-11

Corresponding Author(s): Weihua LI

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2023, 18(2): 32.
Jingyan XIA, Ruyi HUANG, Yixiao LIAO, Jipu LI, Zhuyun CHEN, Weihua LI. Digital twin-assisted gearbox dynamic model updating toward fault diagnosis. Front. Mech. Eng., 2023, 18(2): 32.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-023-0748-0
https://academic.hep.com.cn/fme/CN/Y2023/V18/I2/32

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Abbreviations
FA	Firefly algorithm
FEM	Finite element method
FFT	Fast Fourier transform
LHS	Latin hypercube sampling
LPM	Lumped parameter method
LSM	Least squares method
PHM	Prognostics and health management
PRSM	Polynomial response surface model
RFCD	Rigid–flexible coupling dynamic
RFCM	Rigid–flexible coupling method
RSM	Response surface methodology
Variables
a_i	Amplitude of the exciting force
$a ˉ i$	Amplitude of the vibration response
C_df	Dynamic friction coefficient
C_D	Damping coefficient
C_sf	Static friction coefficient
D_P	Penetration depth
e_F	Force exponent
E	Elastic modulus of gears
f(t)	Excitation force
f(t₁,t₂,t₃)	Cosine similarity between virtual and experimental signals
f_n1, f_n2	Rotation frequencies of input and output gears, respectively
f_z	Mesh frequency
g	gth iteration
h(t)	Transfer function of the gearbox
k	Number of sensitive model parameters
K	Contact stiffness
L	Number of sample points
M	Number of mode order
n	Number of parameters
p	Model parameters in the dynamic model
p_L	Lower bound of the model parameters
p_s	Sensitive model parameters
p_sL	Lower bound of the sensitive model parameters
p_sU	Upper bound of the sensitive model parameters
p_U	Upper bound of the model parameters
r₁, r₂	Equivalent radius
r_ij	Distance between fireflies i and j
R²	Coefficient of determination
R(p)	Difference between the generated and physical signals
t₁	Normalized contact stiffness
t₂	Normalized contact damping coefficient
t₃	Normalized force exponent
V_dt	Dynamic transonic speed
V_st	Static transonic speed
X	Variable matrix of sampling points
X_e	Physical signal in the time domain
X_g	Generated signal in the time domain
$y ˉ$	Mean value of the simulation response
y_i	Result of sample point i based on the complex simulation model
$y ~ i$	Result of sample point i based on the constructed surrogate model
y(t)	Vibration response
Y	Response vector of sampling points
z₁	Tooth number of the driving gear
z₂	Tooth number of the driven gear
α	Random parameter that controls movement randomization
β	Unknown coefficient vector
β₀	Attractiveness factor
ε	Error vector
γ	Brightness absorption coefficient
ν₁, ν₂	Poisson’s ratios of the gears
θ₁	Phase of the exciting force
$θ ˉ i$	Phase of the vibration response
ρ	Density of gears
$?$	Random vector (k-dimensional)

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