Compressive power spectrum sensing for vibration-based output-only system identification of structural systems in the presence of noise

Sub-Nyquist signal-reconstruction-free operational modal analysis and damage detection in the presence of noise

“…Further, with the exception of the work by Park et al 9 , all the above CS methods require computational expensive CS-based signal reconstruction from the compressed (sub-Nyquist) measurements upon wireless transmission. This paper builds on recent work by the authors [13][14][15][16] to accomplish OMA and damage detection directly from compressed measurements of response acceleration stochastic processes (i.e., without signal reconstruction in the time-domain), and without posing any sparsity conditions by means of sub-Nyquist power spectrum blind sampling (PSBS). In particular, PSBS strategies aims to reconstruction of the covariance function of random signals or stochastic processes at all temporal lags of interest.…”

“…Further, it has been shown that PSBS are suitable for spectral recovery of very weak compressed signals buried in high level noise 12,17 . In this respect, the proposed approach is based on non-uniform deterministic multi-coset sampling 18,19 along with a particular PSBS method [13][14][15] . The adopted method approach was first considered by the authors 14,15 for single-sensor spectrum estimation, showing promising results in retrieving the frequency response function of white-noise excited multi-degree-of-freedom systems.…”

Multi-channel sub-Nyquist cross-spectral estimation for modal analysis of vibrating structures

“…which is a generalization of the single device (channel) case considered in [9][12]. In the previous expression, [1]…”

“…In particular, ωn and ζn are the natural frequency and critical damping ratio of the n-th mode, respectively, φni is equal to the φn(xi) mode shape ordinate at a distance xi of point i from the left end of the beam, and δrs=1 for r=s, and δrs=0 for r≠s. All 15 sampling devices considered are identical comprising M=5 branches with a down-sampling parameter N=16 and a common deterministic, non-uniform, and periodic sub-Nyquist multi-coset sampling pattern given by the sequence n = [0 1 2 5 8] T [8], [10][12]. They achieve a compression ratio of M/N≈30%.…”

“…The proposed approach builds on recent work by the authors on power spectrum blind sampling (PSBS) for system identification of white-noise excited structural systems [9], [10], and extends the works in [11], [12], to achieve cross-spectral estimation from simultaneous multiple sensing channels. Specifically, the multi-coset sampling device in [11] is adopted yielding deterministic, non-uniform, periodic samples taken at a sub-Nyquist rate [13].…”