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Condition assessment of retrofitted steel truss bridge through fused Hilbert transform and frequency resolution enhancing techniques

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Abstract

The study aims to determine the variation in the behaviour of different downstream and upstream nodes before and after retrofitting of an old steel truss bridge. The modal frequencies obtained from the vibration response signals are used to determine the improvement in the intactness of various nodes of the bridge. In this study, the Hilbert transform (HT) is applied in combination with modal frequency resolution enhancing signal processing techniques such as Fast Fourier transform (FFT), Multiple Signal Classification (MUSIC) algorithm, Estimation of signal parameters via rotational invariance (ESPRIT) for addressing the issues of additional noise present in the collected vibration response signals. The outcomes of the proposed methodology are compared for before and after retrofitting to observe the improved behaviour of different nodes of the bridge. The concept of sliding window ESPRIT is also applied to observe the variation of the modal frequencies at different nodes of the bridge. The application of HT-ESPRIT showed more robust, denoised and accurate outcomes than HT-MUSIC and HT-FFT techniques. The deficient nodes of the bridge are accurately identified through the outcomes of sliding window-ESPRIT technique.

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Abbreviations

\(A_{i}\) :

Complex amplitude

AR:

Autocorrelation

a(t):

Instantaneous amplitude

C y :

Correlation matrix

d :

Two submatrices distance

\(e^{H} \left( {f_{i} } \right)\) :

Signal vector

\({\text{e}}^{ - i\omega t}\) :

Complex exponentials

e n :

White noise

\({\text{e}}^{{j2\pi f_{k} }}\) :

Eigenvalue exponentials

Hz:

Hertz

H :

Hermitian transpose

\(H\left[ {u\left( t \right)} \right]\) :

Hilbert transform (HT)

\(I_{N - 1}\) :

Identity matrix having order of (N − 1)

\(Q^{{{\text{MUSIC}}}} \left( f \right)\) :

MUSIC pseudospectrum

\(S_{{{\text{sub}}}}\) :

Subspace matrices

S :

Eigenvector matrix

U :

Fourier transform operator

u(t):

Sample signal

\(V_{m + 1}\) :

Noise eigenvector

\(\omega \left( t \right)\) :

Instantaneous frequency

\(\theta \left( t \right)\) :

Instantaneous phase\({\theta \left( t \right) }\)

\(\left( \cdot \right)^{H}\) :

Hermitian operator

\(\varphi\) :

Eigen matrix

\(\sigma^{2}\) :

Variance

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Acknowledgements

The authors would like to thank the Himachal Pradesh Public Works Department, Government of Himachal Pradesh, India for allowing the National Institute of Technology, Hamirpur to conduct the experiment on the steel truss bridge in the state. The authors also thank Dr. Suresh Kumar Walia for providing necessary experimental data for further signal processing.

Funding

The authors declare that the present study is not funded by any source.

Author information

Authors and Affiliations

  1. Civil Engineering Department, National Institute of Technology, Hamirpur, Himachal Pradesh, 177005, India

    Anshul Sharma & Pardeep Kumar

  2. Entrepreneurship Development and Industrial Coordination Department, National Institute of Technical Teachers Training and Research, Chandigarh, 160019, India

    Hemant Kumar Vinayak

  3. Himachal Pradesh Public Works Department, Kangra, Himachal Pradesh, 176001, India

    Suresh Kumar Walia

  4. Electrical Engineering Department, Rajkiya Engineering College Sonbhadra, Robertsganj, Churk, Uttar Pradesh, 231206, India

    Raj Kumar Patel

Authors
  1. Anshul Sharma
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  2. Pardeep Kumar
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  3. Hemant Kumar Vinayak
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  4. Suresh Kumar Walia
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  5. Raj Kumar Patel
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Corresponding author

Correspondence to Anshul Sharma.

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The authors declare that there is no conflict of interest in the context of the publication of this manuscript. In addition, authors have carefully observed the ethical issues of plagiarism, misconduct, data falsification or any misconduct while developing the article.

Appendices

Appendix A

figure a

HT-root MUSIC plots of downstream nodes for before and after retrofitting of the steel truss bridge

figure b

HT-root MUSIC plots of upstream nodes for before and after retrofitting of the steel truss bridge

Appendix B

figure c

HT-ESPRIT plots of downstream nodes for before and after retrofitting of steel truss bridge

figure d

HT-ESPRIT plots of upstream nodes for before and after retrofitting of steel truss bridge

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Sharma, A., Kumar, P., Vinayak, H.K. et al. Condition assessment of retrofitted steel truss bridge through fused Hilbert transform and frequency resolution enhancing techniques. Innov. Infrastruct. Solut. 6, 31 (2021). https://doi.org/10.1007/s41062-020-00396-7

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  • DOI: https://doi.org/10.1007/s41062-020-00396-7

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