Abstract

Each object has unique inherent frequencies and vibration modes, which are known as modal parameters. The modal analysis aims to study the free vibration characteristics of an object under an external force action. In modal analysis, finite element method (FEM) is widely used to build dynamic model structures and solve for modal parameters. Nevertheless, despite its widespread application, FEM does come with certain drawbacks related to computational efficiency. FEM necessitates the construction of stiffness and mass matrices for the structure, alongside an eigenvalue analysis during modal analysis, which can result in extensive computational time. Additionally, meshing the object is a fundamental requirement for FEM, and achieving proper meshing can be a laborious and time-consuming task. In the case of nonlinear problems, FEM demands iterative solutions, with each iteration addressing a linear system. To that end, in this article, we propose a MODAL-DRN-BL framework to improve the computational efficiency against FEM. MODAL-DRN-BL utilizes convolution operation to effectively expand the receptive field and capture vibration information at longer distances. It also handles sparse interaction between features through a broad learning module. Experimental results demonstrate that our proposed MODAL-DRN-BL framework achieves a mean absolute error of 1.49 in modal analysis benchmark ansys apdl (Ansys Parametric Design Language). Moreover, in terms of computational time, the MODAL-DRN-BL framework exhibits significant optimization compared to ansys apdl, resulting in a five-order-of-magnitude improvement in computational efficiency.

References

1.
Peña
,
M.
,
Cerrada
,
M.
,
Medina
,
R.
,
Cabrera
,
D.
, and
Sánchez
,
R. V.
,
2023
, “
Poincaré Plot Features and Statistical Features From Current and Vibration Signals for Fault Severity Classification of Helical Gear Tooth Breaks
,”
ASME J. Comput. Inf. Sci. Eng.
,
23
(
2
), p.
021009
.
2.
Huang
,
Y.
,
Xie
,
Q.
, and
Wang
,
X.
,
2022
, “
Research on Path Planning for Reducing Vibration Fatigue of Precision Equipment Transportation
,”
ASME J. Comput. Inf. Sci. Eng.
,
22
(
1
), p.
011009
.
3.
Fu
,
Z.-F.
, and
He
,
J.
,
2001
,
Modal Analysis
,
Elsevier
.
4.
Ghasemi
,
M. R.
,
Nobahari
,
M.
, and
Shabakhty
,
N.
,
2018
, “
Enhanced Optimization-Based Structural Damage Detection Method Using Modal Strain Energy and Modal Frequencies
,”
Eng. Comput.
,
34
, pp.
637
647
.
5.
Nguyen
,
K.-D.
,
Chan
,
T. H.
, and
Thambiratnam
,
D. P.
,
2016
, “
Structural Damage Identification Based on Change in Geometric Modal Strain Energy–Eigenvalue Ratio
,”
Smart Mater. Struct.
,
25
(
7
), p.
075032
.
6.
Moradi Pour
,
P.
,
Chan
,
T.
, and
Gallage
,
C.
,
2015
, “
An Improved Modal Strain Energy Method for Structural Damage Detection, 2D Simulation
,”
Struct. Eng. Mech.
,
54
(
1
), pp.
105
119
.
7.
Khatir
,
S.
,
Wahab
,
M. A.
,
Boutchicha
,
D.
, and
Khatir
,
T.
,
2019
, “
Structural Health Monitoring Using Modal Strain Energy Damage Indicator Coupled With Teaching-Learning-Based Optimization Algorithm and Isogoemetric Analysis
,”
J. Sound Vib.
,
448
, pp.
230
246
.
8.
Pooya
,
S. M. H.
, and
Massumi
,
A.
,
2022
, “
A Novel Damage Detection Method in Beam-Like Structures Based on the Relation Between Modal Kinetic Energy and Modal Strain Energy and Using Only Damaged Structure Data
,”
J. Sound Vib.
,
530
, p.
116943
.
9.
Hakim
,
S.
, and
Razak
,
H. A.
,
2014
, “
Modal Parameters Based Structural Damage Detection Using Artificial Neural Networks—A Review
,”
Smart Struct. Syst.
,
14
(
2
), pp.
159
189
.
10.
Khatir
,
A.
,
Capozucca
,
R.
,
Khatir
,
S.
, and
Magagnini
,
E.
,
2022
, “
Vibration-Based Crack Prediction on a Beam Model Using Hybrid Butterfly Optimization Algorithm With Artificial Neural Network
,”
Front. Struct. Civil Eng.
,
16
(
8
), pp.
976
989
.
11.
Al Thobiani
,
F.
,
Khatir
,
S.
,
Benaissa
,
B.
,
Ghandourah
,
E.
,
Mirjalili
,
S.
, and
Wahab
,
M. A.
,
2022
, “
A Hybrid PSO and Grey Wolf Optimization Algorithm for Static and Dynamic Crack Identification
,”
Theor. Appl. Fract. Mech.
,
118
, p.
103213
.
12.
Tan
,
Z. X.
,
Thambiratnam
,
D.
,
Chan
,
T.
, and
Razak
,
H. A.
,
2017
, “
Detecting Damage in Steel Beams Using Modal Strain Energy Based Damage Index and Artificial Neural Network
,”
Eng. Failure Anal.
,
79
, pp.
253
262
.
13.
Tan
,
Z. X.
,
Thambiratnam
,
D. P.
,
Chan
,
T. H.
,
Gordan
,
M.
, and
Abdul Razak
,
H.
,
2020
, “
Damage Detection in Steel-Concrete Composite Bridge Using Vibration Characteristics and Artificial Neural Network
,”
Struct. Infrastruct. Eng.
,
16
(
9
), pp.
1247
1261
.
14.
Nick
,
H.
,
Aziminejad
,
A.
,
Hosseini
,
M. H.
, and
Laknejadi
,
K.
,
2021
, “
Damage Identification in Steel Girder Bridges Using Modal Strain Energy-Based Damage Index Method and Artificial Neural Network
,”
Eng. Failure Anal.
,
119
, p.
105010
.
15.
Jayasundara
,
N.
,
Thambiratnam
,
D.
,
Chan
,
T.
, and
Nguyen
,
A.
,
2020
, “
Damage Detection and Quantification in Deck Type Arch Bridges Using Vibration Based Methods and Artificial Neural Networks
,”
Eng. Failure Anal.
,
109
, p.
104265
.
16.
Sadeghi
,
F.
,
Yu
,
Y.
,
Zhu
,
X.
, and
Li
,
J.
,
2021
, “
Damage Identification of Steel-Concrete Composite Beams Based on Modal Strain Energy Changes Through General Regression Neural Network
,”
Eng. Struct.
,
244
, p.
112824
.
17.
Ghannadi
,
P.
, and
Kourehli
,
S. S.
,
2021
, “
An Effective Method for Damage Assessment Based on Limited Measured Locations in Skeletal Structures
,”
Adv. Struct. Eng.
,
24
(
1
), pp.
183
195
.
18.
Paral
,
A.
,
Singha Roy
,
D. K.
, and
Samanta
,
A. K.
,
2019
, “
Application of a Mode Shape Derivative-Based Damage Index in Artificial Neural Network for Structural Damage Identification in Shear Frame Building
,”
J. Civil Struct. Health Monitor.
,
9
, pp.
411
423
.
19.
Teng
,
S.
,
Chen
,
G.
,
Gong
,
P.
,
Liu
,
G.
, and
Cui
,
F.
,
2020
, “
Structural Damage Detection Using Convolutional Neural Networks Combining Strain Energy and Dynamic Response
,”
Meccanica
,
55
, pp.
945
959
.
20.
Qin
,
M.
, and
Chen
,
H.
,
2021
, “
Operational Modal Analysis Based on Neural Network With Singular Value Decomposition
,”
2021 Global Reliability and Prognostics and Health Management (PHM-Nanjing)
,
Nanjing, China
,
Oct. 15–17
,
IEEE
, pp.
1
7
.
21.
Maurizi
,
M.
,
Gao
,
C.
, and
Berto
,
F.
,
2022
, “
Predicting Stress, Strain and Deformation Fields in Materials and Structures With Graph Neural Networks
,”
Sci. Rep.
,
12
(
1
), p.
21834
.
22.
Yang
,
Z.
,
Yu
,
C.-H.
,
Guo
,
K.
, and
Buehler
,
M. J.
,
2021
, “
End-to-End Deep Learning Method to Predict Complete Strain and Stress Tensors for Complex Hierarchical Composite Microstructures
,”
J. Mech. Phys. Solids
,
154
, p.
104506
.
23.
Nie
,
Z.
,
Jiang
,
H.
, and
Kara
,
L. B.
,
2020
, “
Stress Field Prediction in Cantilevered Structures Using Convolutional Neural Networks
,”
ASME J. Comput. Inf. Sci. Eng.
,
20
(
1
), p.
011002
.
24.
Bhaduri
,
A.
,
Gupta
,
A.
, and
Graham-Brady
,
L.
,
2022
, “
Stress Field Prediction in Fiber-Reinforced Composite Materials Using a Deep Learning Approach
,”
Compos. Part B: Eng.
,
238
, p.
109879
.
25.
Yang
,
C.
,
Kim
,
Y.
,
Ryu
,
S.
, and
Gu
,
G. X.
,
2020
, “
Prediction of Composite Microstructure Stress-Strain Curves Using Convolutional Neural Networks
,”
Mater. Des.
,
189
, p.
108509
.
26.
Jiang
,
H.
,
Nie
,
Z.
,
Yeo
,
R.
,
Farimani
,
A. B.
, and
Kara
,
L. B.
,
2021
, “
StressGAN: A Generative Deep Learning Model for Two-Dimensional Stress Distribution Prediction
,”
ASME J. Appl. Mech.
,
88
(
5
), p.
051005
.
27.
He
,
K.
,
Zhang
,
X.
,
Ren
,
S.
, and
Sun
,
J.
,
2016
, “
Deep Residual Learning for Image Recognition
,”
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
,
Las Vegas, NV
,
June 27–30
, pp.
770
778
.
28.
Yu
,
F.
,
Koltun
,
V.
, and
Funkhouser
,
T.
,
2017
, “
Dilated Residual Networks
,”
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
,
Honolulu, HI
,
July 21–26
, pp.
472
480
.
29.
Yu
,
F.
, and
Koltun
,
V.
,
2015
, “Multi-scale Context Aggregation by Dilated Convolutions,” preprint arXiv:1511.07122.
30.
Chen
,
C. P.
, and
Liu
,
Z.
,
2017
, “
Broad Learning System: An Effective and Efficient Incremental Learning System Without the Need for Deep Architecture
,”
IEEE Trans. Neural Netw. Learn. Syst.
,
29
(
1
), pp.
10
24
.
31.
Huber
,
P. J.
,
1992
, “Robust Estimation of a Location Parameter,”
Breakthroughs in Statistics: Methodology and Distribution
,
Springer
,
New York
, pp.
492
518
.
32.
Krichen
,
M.
,
2023
, “
Generative Adversarial Networks
,”
2023 14th International Conference on Computing Communication and Networking Technologies (ICCCNT)
,
Delhi, India
,
July 6–8
,
IEEE
, pp.
1
7
.
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