Condition assessment of retrofitted steel truss bridge through fused Hilbert transform and frequency resolution enhancin
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TECHNICAL PAPER
Condition assessment of retrofitted steel truss bridge through fused Hilbert transform and frequency resolution enhancing techniques Anshul Sharma1 · Pardeep Kumar1 · Hemant Kumar Vinayak2 · Suresh Kumar Walia3 · Raj Kumar Patel4 Received: 11 May 2020 / Accepted: 28 October 2020 © Springer Nature Switzerland AG 2020
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. Keyword Steel bridge · Retrofitting · HT · FFT · MUSIC · ESPRIT · Sliding window HT-ESPRIT List of symbols Ai Complex amplitude AR Autocorrelation * Anshul Sharma [email protected] Pardeep Kumar [email protected] Hemant Kumar Vinayak [email protected] Suresh Kumar Walia [email protected] Raj Kumar Patel [email protected] 1
Civil Engineering Department, National Institute of Technology, Hamirpur, Himachal Pradesh 177005, India
2
Entrepreneurship Development and Industrial Coordination Department, National Institute of Technical Teachers Training and Research, Chandigarh 160019, India
3
Himachal Pradesh Public Works Department, Kangra, Himachal Pradesh 176001, India
4
Electrical Engineering Department, Rajkiya Engineering College Sonbhadra, Robertsganj, Churk, Uttar Pradesh 231206, India
a(t) Instantaneous amplitude Cy Correlation matrix d Two submatrices distance ( ) eH fi Signal vector e−i𝜔t Complex exponentials en White noise ej2𝜋fk Eigenvalue exponentials Hz Hertz H Hermitian transpose H[u(t)] Hilbert transform (HT) IN−1 Identity matrix having order of (N − 1) QMUSIC (f ) MUSIC pseudospectrum Ssub Subspace matrices S Eigenvector matrix U Fourier transform operator u(t) Sample signal Vm+1 Noise eigenvector 𝜔(t) Instantaneous frequency 𝜃(t) Instantaneous phase𝜃(t) (⋅)H Hermitian operator 𝜑 Eigen matrix 𝜎 2 Variance
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Introduction The health of a structure
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