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Motivated by a need to reduce energy consumption in wireless sensors for vibration-based structural health monitoring
(SHM) associated with data acquisition and transmission, this paper puts forth a novel approach for undertaking
operational modal analysis (OMA) and damage localization relying on compressed vibrations measurements sampled at
rates well below the Nyquist rate. Specifically, non-uniform deterministic sub-Nyquist multi-coset sampling of response
acceleration signals in white noise excited linear structures is considered in conjunction with a power spectrum blind
sampling/estimation technique which retrieves/samples the power spectral density matrix from arrays of sensors directly
from the sub-Nyquist measurements (i.e., in the compressed domain) without signal reconstruction in the time-domain
and without posing any signal sparsity conditions. The frequency domain decomposition algorithm is then applied to the
power spectral density matrix to extract natural frequencies and mode shapes as a standard OMA step. Further, the modal
strain energy index (MSEI) is considered for damage localization based on the mode shapes extracted directly from the
compressed measurements. The effectiveness and accuracy of the proposed approach is numerically assessed by
considering simulated vibration data pertaining to a white-noise excited simply supported beam in healthy and in 3
damaged states, contaminated with Gaussian white noise. Good accuracy is achieved in estimating mode shapes
(quantified in terms of the modal assurance criterion) and natural frequencies from an array of 15 multi-coset devices
sampling at a 70% slower than the Nyquist frequency rate for SNRs as low as 10db. Damage localization of equal
level/quality is also achieved by the MSEI applied to mode shapes derived from noisy sub-Nyquist (70% compression)
and Nyquist measurements for all damaged states considered. Overall, the furnished numerical results demonstrate that
the herein considered sub-Nyquist sampling and multi-sensor power spectral density estimation techniques coupled with
standard OMA and damage detection approaches can achieve effective SHM from significantly fewer noisy acceleration
measurements.
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