Skip to main content
SpringerLink
Log in

Transfer path analysis using deep neural networks trained by measured operational responses

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

We present an operational transfer path analysis (OTPA) formulation based on deep learning to solve structural problems. Deep neural networks (DNNs) with fully connected or convolutional layers model the transfer function from interfacial joints to the responses of points of interest in terms of forces, thereby eliminating the cross-coupling effects of conventional OTPA methods. Using an operational dataset, phase and cross-spectrum augmentation procedures were applied to train DNNs by reference to the required path contributions. A test structure with two plates and three transfer paths was used to experimentally validate the OTPA framework. The operational responses were quantified and used to train DNNs that engage in OTPA; we evaluated various hyperparameters. The path contributions were obtained from DNNs that had been trained to follow the required OTPA procedure and compared to those of classical transfer path analysis (TPA). Experimental identification of the path contributions revealed that the new OTPA method was as accurate as the classical TPA method and had good overall task efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

C ij :

Contribution through the j-th transfer path

f :

Force vector

H :

Receptance matrix

\({\boldsymbol{\tilde H}}\) :

Modified transfer function matrix

k :

Joint stiffness

M :

Number of ROIs

N :

Number of paths

ϰ :

Training dataset

ϰ 0 :

Measured dataset

ϰ 1 :

Phase-augmented dataset

ϰ 2 :

Input cross-spectra-augmented dataset

ϰ 3 :

Output cross-spectra-augmented dataset

R :

Response of interest (ROI)

T :

Transformation function

U :

Input layer vector or matrix

u :

Displacement vector

Δu I :

Relative displacement vector at interface

γ :

Output layer vector

η :

Loss factor

ω :

Frequency

References

  1. D.-H. Lee and W.-S. Hwang, Parametric optimization of complex systems using a multi-domain FRF-based substructuring method, Computers and Structures, 81(22–23) (2003) 2249–2257.

    Article  Google Scholar 

  2. H. Van der Auweraer, P. Mas, S. Dom, A. Vecchio, K. Janssens and P. Van de Ponseele, Transfer path analysis in the critical path of vehicle refinement: the role of fast, hybrid and operational path analysis, SAE Technical Paper (2007) 2007-01-2352.

  3. M. V. van der Seijs, D. de Klerk and D. J. Rixen, General framework for transfer path analysis: History, theory and classification of techniques, Mechanical Systems and Signal Processing, 68 (2016) 217–244.

    Article  Google Scholar 

  4. D.-H. Lee, W.-S. Hwang and M.-E. Kim, Booming noise analysis in a passenger car using a hybrid-integrated approach, SAE Transactions (2000) 1069–1075.

  5. K. Wyckaert and H. Van der Auweraer, Operational analysis, transfer path analysis, modal analysis: tools to understand road noise problems in cars, SAE Technical Paper (1995) 951151.

  6. A. Oktav, G. Anlaş and Ç. Yılmaz, Assessment of vehicle noise variability through structural transfer path analysis, International Journal of Vehicle Design, 71(1–4) (2016) 300–320.

    Article  Google Scholar 

  7. M. H. Janssens, J. W. Verheij and D. Thompson, The use of an equivalent forces method for the experimental quantification of structural sound transmission in ships, Journal of Sound and Vibration, 226(2) (1999) 305–328.

    Article  Google Scholar 

  8. D. De Klerk and A. Ossipov, Operational transfer path analysis: Theory, guidelines and tire noise application, Mechanical Systems and Signal Processing, 24(7) (2010) 1950–1962.

    Article  Google Scholar 

  9. K. Noumura and J. Yoshida, Method of transfer path analysis for vehicle interior sound with no excitation experiment, FISITA2006 Proceedings, Yokohama, Japan (2006) 1–10.

  10. J. Putner, H. Fastl, M. Lohrmann, A. Kaltenhauser and F. Ullrich, Operational transfer path analysis predicting contributions to the vehicle interior noise for different excitations from the same sound source, The Proceedings of 41st International Congress and Exposition on Noise Control Engineering, INTER-NOISE, New York City, USA (2012).

    Google Scholar 

  11. K. Janssens, P. Gajdatsy, L. Gielen, P. Mas, L. Britte, W. Desmet and H. Van der Auweraer, OPAX: a new transfer path analysis method based on parametric load models, Mechanical Systems and Signal Processing, 25(4) (2011) 1321–1338.

    Article  Google Scholar 

  12. P. Gajdatsy, K. Janssens, L. Gielen, P. Mas and H. Van Der Auweraer, Critical assessment of operational path analysis: mathematical problems of transmissibility estimation, Journal of the Acoustical Society of America, 123(5) (2008) 3869.

    Article  Google Scholar 

  13. P. Gajdatsy, K. Janssens, L. Gielen, P. Mas and H. Van der Auweraer, Critical assessment of operational path analysis: effect of neglected paths, The Proceedings of The Proceedings of the 15th International Congress on Sound and Vibration, Daejean, Korea (2008) 1090–1097.

  14. P. Gajdatsy, K. Janssens, L. Gielen, P. Mas and H. Van Der Auweraer, Critical assessment of operational path analysis: effect of coupling between path inputs, Journal of the Acoustical Society of America, 123(5) (2008) 3876–3876.

    Article  Google Scholar 

  15. D. Tcherniak, Application of Transmissibility Matrix method to structure borne path contribution analysis, The Proceedings of Proceedings of NAG/DAGA Conference, Rotterdam, Holland (2009).

  16. I. Goodfellow, Y. Bengio and A. Courville, Deep Learning, MIT Press (2016).

  17. B. Z. Cunha, C. Droz, A.-M. Zine, S. Foulard and M. Ichchou, A review of machine learning methods applied to structural dynamics and vibroacoustic, Mechanical Systems and Signal Processing, 200 (2023) 110535.

    Article  Google Scholar 

  18. B. Rezaeianjouybari and Y. Shang, Deep learning for prognostics and health management: state of the art, challenges, and opportunities, Measurement, 163 (2020) 107929.

    Article  Google Scholar 

  19. K. Saigusa, F. Chauvicourt and H. Van der Auweraer, Application of neural networks for transfer path analysis, The Proceedings of The International Conference on Structural Engineering Dynamics (ICEDyn 2019), Viana do Castelo, Portugal (2019).

  20. D. Lee and J. W. Lee, Operational transfer path analysis based on deep neural network: numerical validation, Journal of Mechanical Science and Technology, 34(3) (2020) 1023–1033.

    Article  Google Scholar 

  21. D. E. Tsokaktsidis, C. Nau, M. Maeder and S. Marburg, Using rectified linear unit and swish based artificial neural networks to describe noise transfer in a full vehicle context, The Journal of the Acoustical Society of America, 150(3) (2021) 2088–2105.

    Article  Google Scholar 

  22. U. Park and Y. J. Kang, Contribution analysis of road noise with transfer path analysis based on neural network, The Proceedings of INTER-NOISE and NOISE-CON Congress and Conference Proceedings (2023) 2373–2378.

  23. A. N. Thite and D. J. Thompson, The quantification of structure-borne transmission paths by inverse methods, part 1: improved singular value rejection methods, Journal of Sound and Vibration, 264(2) (2003) 411–431.

    Article  Google Scholar 

  24. Y. LeCun, L. Bottou, Y. Bengio and P. Haffner, Gradient-based learning applied to document recognition, Proceedings of the IEEE, 86(11) (1998) 2278–2324.

    Article  Google Scholar 

  25. S. Kiranyaz, T. Ince and M. Gabbouj, Real-time patient-specific ECG classification by 1-D convolutional neural networks, IEEE Transactions on Biomedical Engineering, 63(3) (2015) 664–675.

    Article  Google Scholar 

  26. S. Kiranyaz, O. Avci, O. Abdeljaber, T. Ince, M. Gabbouj and D. J. Inman, 1D convolutional neural networks and applications: a survey, Mechanical Systems and Signal Processing, 151 (2021) 107398.

    Article  Google Scholar 

  27. W. Cheng, Y. Chu, X. Chen, G. Zhou, D. Blamaud and J. Lu, Operational transfer path analysis with crosstalk cancellation using independent component analysis, Journal of Sound and Vibration, 473 (2020) 115224.

    Article  Google Scholar 

  28. F. Chollet, Keras: the python deep learning library, Astrophysics Source Code Library (2018).

  29. M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving and M. Isard, Tensorflow: a system for large-scale machine learning, The Proceedings of 12th USENIX Symposium on Operating Systems Design and Implementation, Savannah, USA (2016) 265–283.

  30. T. Tieleman and G. Hinton, Lecture 6.5-rmsprop: divide the gradient by a running average of its recent magnitude, Coursera: Neural Networks for Machine Learning, 4(2) (2012) 26–31.

    Google Scholar 

Download references

Acknowledgments

This work was supported by a grant from the National Research Foundation of Korea (NRF) funded by the Korean government (MEST; grant no. NRF-2022R1A2C1006938).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Dongeui University, Busan, 47340, Korea

    Dooho Lee & Yun-Yeong Park

Authors
  1. Dooho Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yun-Yeong Park
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dooho Lee.

Additional information

Dooho Lee received his B.S. degree from Seoul National University (Korea) in 1988, his M.S. from KAIST (Korea) in 1990, and his Ph.D. from KAIST (Korea) in 1994. He worked for Samsung Motors, Inc. (1995-1999) and is currently a Professor at Dongeui University. His research includes optimization of structural-acoustic systems, evaluation of uncertainty propagation in dynamic systems, and the sound transfer characteristics of human hearing.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, D., Park, YY. Transfer path analysis using deep neural networks trained by measured operational responses. J Mech Sci Technol 37, 5739–5750 (2023). https://doi.org/10.1007/s12206-023-1013-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-023-1013-5

Keywords

Search

Navigation